question stringlengths 326 14.9k | answer stringlengths 1 664 | taskname stringclasses 36
values | doc_id int64 0 670 | o3-mini-high_correct bool 2
classes | o4-mini-high_correct bool 2
classes |
|---|---|---|---|---|---|
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{\frac{m_{2} \cos \theta \left|m_{2} \sin \theta - m_{1}\right|}{M\left(m_{1} + m_{2}\right) + 2 m_{1} m_{2}(1 + \sin \theta) + m_{2}^{2} \cos^{2} \theta}} | ugphysics_ClassicalMechanics | 56 | true | false |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{-\frac{m h^{2}}{2 r^{2}}} | ugphysics_ClassicalMechanics | 59 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \[
\boxed{z_{\text{max}} = \max \left(a, \frac{v^{2}}{2g}\right)}
\] | ugphysics_ClassicalMechanics | 70 | false | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{\frac{I ndk^{2} A}{16E^{2} r^{2} \sin^{4}\left(\frac{\alpha}{2}\right)}} | ugphysics_ClassicalMechanics | 88 | false | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \boxed{458} | ugphysics_ClassicalMechanics | 123 | true | false |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{r = \left[2\left(t^2 + \sqrt{6} t + 2\right)\right]^{1/2}} | ugphysics_ClassicalMechanics | 142 | false | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{v = v_{0} - \left(\frac{\mu m g}{\rho A}\right)^{1/2}} | ugphysics_ClassicalMechanics | 170 | true | false |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \boxed{\frac{\pi}{2}} | ugphysics_ClassicalMechanics | 175 | true | true |
The following is an open-ended problem from Classical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \[
\boxed{3a \sqrt{\frac{3k}{m}}}
\] | ugphysics_ClassicalMechanics | 181 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be one option of a multiple choice question. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables a... | \boxed{C} | ugphysics_Electrodynamics | 2 | false | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formul... | \boxed{0.13} | ugphysics_Electrodynamics | 70 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{n_{e} < \frac{\varepsilon_{0} m_{e} \omega^{2}}{e^{2}}} | ugphysics_Electrodynamics | 73 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{-\frac{e \rho r}{2 \varepsilon_{0} \gamma^{2}} \boldsymbol{e}_{r}} | ugphysics_Electrodynamics | 88 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solut... | \[
\boxed{\boldsymbol{B} = -\frac{\varepsilon-\varepsilon_{0}}{\varepsilon+2\varepsilon_{0}} \cdot \frac{\omega^{2} a^{3}}{c^{3} r} E_{0} e^{i(k r-\omega t)} \sin \theta \boldsymbol{e}_{\phi}, \boldsymbol{E} = -\frac{\varepsilon-\varepsilon_{0}}{\varepsilon+2\varepsilon_{0}} \cdot \frac{\omega^{2} a^{3}}{c^{2} r} E_{0}... | ugphysics_Electrodynamics | 95 | true | false |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The problem has multiple answers, each of them should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the... | \boxed{2.1 \times 10^{7}, 1.5 \times 10^{7}} | ugphysics_Electrodynamics | 103 | true | false |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{\frac{4 n}{(1+n)^{2}+n^{2} \sigma^{2} / 4 \varepsilon^{2} \omega^{2}}} | ugphysics_Electrodynamics | 104 | false | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \[\boxed{\frac{v q^{2} r^{2}}{4 \pi^{2} \varepsilon_{0} c^{2} R^{4} l^{2}} \boldsymbol{e}_{x}, \frac{v q^{2}}{4 \pi^{2} \varepsilon_{0} c^{2} r^{2} l^{2}} \boldsymbol{e}_{x}}\] | ugphysics_Electrodynamics | 109 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formul... | \boxed{\frac{\mu_{0} q^{2} a^{2} \omega^{4}}{6 \pi c}} | ugphysics_Electrodynamics | 116 | false | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{\frac{e E_{0}}{m\left(\omega^{2} - \omega_{0}^{2}\right)} e^{-\mathrm{i} \omega t}} | ugphysics_Electrodynamics | 118 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{\frac{e^{2}}{32 \pi^{2} \varepsilon_{0} c}\left|\dot{\boldsymbol{\beta}}_{0}\right|^{2} \sin^{2} \theta} | ugphysics_Electrodynamics | 128 | false | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formu... | \boxed{E_{1x} \mathrm{e}^{\mathrm{i} k_{1} d}+E_{1x}^{\prime} \mathrm{e}^{-\mathrm{i} k_{1} d}=E_{1x}^{\prime \prime} \mathrm{e}^{\mathrm{i} k d}, E_{1y} \mathrm{e}^{\mathrm{i} k_{1} d}+E_{1y}^{\prime} \mathrm{e}^{-\mathrm{i} k_{1} d}=E_{1y}^{\prime \prime} \mathrm{e}^{\mathrm{i} k d}, E_{1x} \mathrm{e}^{\mathrm{i} k_{... | ugphysics_Electrodynamics | 143 | true | false |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The problem has multiple answers, with the answers in order being an equation, an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent... | \boxed{F_{\mathrm{s}} = \frac{1}{6 \pi \varepsilon_{0}} \cdot \frac{e^2}{c^3} \ddot{v}, \ F_{\mathrm{s}} = -\frac{1}{6 \pi \varepsilon_{0}} \cdot \frac{e^2 \omega_{0}^2}{c^3} v} | ugphysics_Electrodynamics | 144 | true | false |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{\boldsymbol{B}(\boldsymbol{r}, t) = \frac{\mathrm{i} \omega^{2} P \mathrm{e}^{\mathrm{i}(k r - \omega t)}}{2 \pi \varepsilon_{0} c^{3} r} \sin \theta \sin (\pi \cos \theta) \boldsymbol{e}_{\varphi}, \boldsymbol{E}(\boldsymbol{r}, t) = \frac{\mathrm{i} \omega^{2} P \mathrm{e}^{\mathrm{i}(k r - \omega t)}}{2 \pi \... | ugphysics_Electrodynamics | 150 | true | false |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solut... | \[
\boxed{\boldsymbol{B}(\boldsymbol{r}, t) =-\frac{\mu_{0} q^{2}}{4 \pi m r c} \mathrm{e}^{\mathrm{i}(k r-\omega t)} \boldsymbol{e}_{\mathrm{r}} \times \boldsymbol{E}_{0}, \boldsymbol{E}(\boldsymbol{r}, t) =\frac{\mu_{0} q^{2}}{4 \pi m r} \mathrm{e}^{\mathrm{i}(k r-\omega t)}\left[\left(\boldsymbol{E}_{0} \cdot \bolds... | ugphysics_Electrodynamics | 156 | true | true |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{\frac{e^{2} R^{2} \omega_{0}^{4}}{32 \pi^{2} \varepsilon_{0} c^{3}}\left(1+\cos^{2} \theta\right)} | ugphysics_Electrodynamics | 161 | true | false |
The following is an open-ended problem from Electrodynamics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formul... | \boxed{\frac{a^{6} \omega^{4}}{c^{4}}\left(\frac{\varepsilon-\varepsilon_{0}}{\varepsilon+2 \varepsilon_{0}}\right)^{2} \sin^2 \theta} | ugphysics_Electrodynamics | 169 | true | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{1} | ugphysics_GeometricalOptics | 8 | true | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{2.08} | ugphysics_GeometricalOptics | 22 | true | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{250} | ugphysics_GeometricalOptics | 31 | false | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the ... | \boxed{u_{1}=\frac{f_{1} d}{d-\left(f_{1}+f_{2}\right)}} | ugphysics_GeometricalOptics | 36 | false | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{\frac{R}{2}} | ugphysics_GeometricalOptics | 39 | true | false |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in th... | \boxed{\left[\frac{1}{n_{2}}, \infty\right)} | ugphysics_GeometricalOptics | 44 | false | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The problem has multiple answers, each of them should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent ... | \boxed{-5, 1.3} | ugphysics_GeometricalOptics | 47 | true | false |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The answer of The problem should be a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in th... | \boxed{\left[\frac{1}{n_{1}}, \infty\right)} | ugphysics_GeometricalOptics | 50 | false | true |
The following is an open-ended problem from Geometrical Optics of the undergraduate-level Physics. The problem has multiple answers, with the answers in order being either True or False, a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX forma... | \boxed{No, (9.00, \infty)} | ugphysics_GeometricalOptics | 52 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{\frac{k \hbar^{2}}{mg} = 1 - \mathrm{e}^{-2ka}} | ugphysics_QuantumMechanics | 22 | false | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and f... | \boxed{E_{n}=\frac{\hbar^{2}}{8 I}\left(n-\frac{q \Phi}{\pi \hbar}\right)^{2}, \psi_{n}(\theta)=\frac{1}{\sqrt{4 \pi}} \mathrm{e}^{\mathrm{i} \frac{n}{2} \theta}} | ugphysics_QuantumMechanics | 41 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and form... | \boxed{1-\frac{3}{4Z^{2}}} | ugphysics_QuantumMechanics | 45 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{\lambda^{\prime} = \lambda + \Delta \lambda, n\left(\lambda^{\prime}\right) = n + \lambda n \frac{\mathrm{d} n}{\mathrm{~d} \lambda} \cdot \frac{v}{c}} | ugphysics_QuantumMechanics | 47 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{E = V_{l}\left(r_{0}\right) + \left(v+\frac{1}{2}\right) \hbar \omega} | ugphysics_QuantumMechanics | 52 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and form... | \boxed{\frac{A^{2} m^{2} e^{2}}{9 \hbar^{4}}} | ugphysics_QuantumMechanics | 74 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{\hat{L}_{a}^{3} = \hat{L}_{a}, \hat{L}_{a}^{5} = 5 \hat{L}_{a}^{3} - 4 \hat{L}_{a}} | ugphysics_QuantumMechanics | 89 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \[
\boxed{\left\langle\frac{1}{r^2}\right\rangle = \frac{1}{\left(l+\frac{1}{2}\right) n^3} \frac{Z^2}{a_0^2}}
\] | ugphysics_QuantumMechanics | 97 | false | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the sol... | \boxed{\alpha_{2} = \tan^{-1} \left(\frac{k_{1}}{k_{2}}\right)} | ugphysics_QuantumMechanics | 100 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and for... | \boxed{\left[-\frac{\hbar^{2}}{2 m} \frac{\mathrm{d}^{2}}{\mathrm{d} x^{2}} + V(x, t)\right] \psi(x, t) = \mathrm{i} \hbar \frac{\partial}{\partial t} \psi(x, t), \left[-\frac{\hbar^{2}}{2 m} \frac{\mathrm{d}^{2}}{\mathrm{d} x^{\prime 2}} + V^{\prime}\left(x^{\prime}, t\right)\right] \psi\left(x^{\prime}, t\right) = \m... | ugphysics_QuantumMechanics | 105 | true | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{\frac{1}{2} \hbar\left(\omega_{1} + \omega_{2}\right) + \frac{3}{2} \hbar \omega_{3} - B \mu^{2}} | ugphysics_QuantumMechanics | 136 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{8 \sum_{n=1}^{\infty} \sqrt{\frac{30}{l}} \cdot \frac{1}{(2n+1)^{3}\pi^{3}} \sin \left(\frac{(2n+1)\pi x}{l}\right) e^{-\frac{\hbar}{2m}\left(\frac{(2n+1)\pi}{l}\right)^{2} t}} | ugphysics_QuantumMechanics | 149 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \[
\boxed{\cos^{2} \left( \frac{\omega t}{2} + \frac{\pi}{4} \right)}
\] | ugphysics_QuantumMechanics | 155 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and form... | \boxed{4 E_{0}+4 c_{2}-\frac{3}{2} c_{1}} | ugphysics_QuantumMechanics | 157 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{\frac{e}{2 m c} \boldsymbol{H} \times \boldsymbol{\mu}} | ugphysics_QuantumMechanics | 173 | false | true |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{\varphi(p)=\sqrt{2 \pi \hbar}[A \delta(p-\hbar k)+B \delta(p+\hbar k)]-\frac{2 m V_{0}}{\sqrt{2 \pi \hbar}} \sum_{n} \frac{\psi(n a)}{p^{2}-\hbar^{2} k^{2}} \mathrm{e}^{-\mathrm{i} p n a / \hbar}}
``` | ugphysics_QuantumMechanics | 186 | true | false |
The following is an open-ended problem from Quantum Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and form... | \[
\boxed{\frac{\mu^{2} \varepsilon^{2} I}{\hbar^{2}} \cdot \frac{1}{4 m^{2} - 1}}
\] | ugphysics_QuantumMechanics | 198 | false | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas u... | \boxed{v = a t^{\prime} \left[1+\left(\frac{a t^{\prime}}{c}\right)^2\right]^{-1/2}, a_x^{\prime} = \gamma a} | ugphysics_Relativity | 4 | true | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas... | \boxed{\frac{1}{2} mc^2 \frac{\sqrt{1 - \beta^2}}{1 - \beta\cos\theta}, \frac{1}{2} mc^2 \frac{1 + \beta^2 - 2\beta\cos\theta}{(1 - \beta\cos\theta) \sqrt{1 - \beta^2}}} | ugphysics_Relativity | 15 | true | false |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the soluti... | \boxed{( - \infty, 1.48 \times 10^{3} )} | ugphysics_Relativity | 17 | false | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solution p... | \[
\boxed{\theta = 2 \arccos \sqrt{\frac{E_0 + m_0 c^2}{E_0 + 3 m_0 c^2}}}
\] | ugphysics_Relativity | 23 | true | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas us... | \boxed{90^\circ} | ugphysics_Relativity | 37 | false | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas us... | \boxed{-\frac{2v}{1+\frac{v^{2}}{c^{2}}}} | ugphysics_Relativity | 38 | false | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas u... | \boxed{\dot{x} = \frac{v_{0}}{\sqrt{1-\left(\frac{v_{0}}{c}\right)^{2}}} \sqrt{\frac{c^{2}}{c^{2}+k}}, \dot{y} = \frac{F t}{m} \sqrt{\frac{c^{2}}{c^{2}+k}}} | ugphysics_Relativity | 51 | false | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solution... | \boxed{v^{\prime} = \sqrt{v^{2} + v^{2}\left(1 - \frac{v^{2}}{c^{2}}\right)}} | ugphysics_Relativity | 69 | true | false |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solution... | \boxed{\frac{c+v}{c-v} I_i} | ugphysics_Relativity | 87 | true | false |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas us... | \boxed{\frac{1}{\sqrt{1 - \left(\frac{500}{3 \times 10^{8}}\right)^{2}}}} | ugphysics_Relativity | 94 | true | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solution... | \boxed{\frac{c \sqrt{p^{2} + m_{0}^{2} c^{2}} - m_{0} c^{2}}{p}} | ugphysics_Relativity | 98 | false | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas us... | \boxed{6 \times 10^{9}} | ugphysics_Relativity | 105 | false | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas u... | \boxed{\alpha=\left[1-\left(\frac{G M m}{J c}\right)^{2}\right]^{\frac{1}{2}}, r_{0}=\frac{(J c)^{2}-(G M m)^{2}}{G M m E}} | ugphysics_Relativity | 148 | true | false |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solution... | \boxed{c \sqrt{m_0^2 c^2+(\boldsymbol{p}-q \boldsymbol{A})^2}+q \phi} | ugphysics_Relativity | 151 | false | true |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solution p... | \boxed{\frac{\mathrm{d} \rho}{\mathrm{d} s}=\sqrt{1-U(\rho)}} | ugphysics_Relativity | 163 | true | false |
The following is an open-ended problem from Relativity of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas us... | \boxed{3.7 \times 10^{3}} | ugphysics_Relativity | 171 | true | false |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{3.33 \times 10^{15}} | ugphysics_SemiconductorPhysics | 69 | true | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be one option of a multiple choice question. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the varia... | \boxed{C} | ugphysics_SemiconductorPhysics | 97 | true | false |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be one option of a multiple choice question. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the varia... | \boxed{c} | ugphysics_SemiconductorPhysics | 103 | true | false |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be either True or False. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas us... | \boxed{Yes} | ugphysics_SemiconductorPhysics | 104 | true | false |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{1.8 \times 10^{16}} | ugphysics_SemiconductorPhysics | 109 | true | false |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{-1.28 \times 10^{-5}} | ugphysics_SemiconductorPhysics | 111 | false | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{38.4} | ugphysics_SemiconductorPhysics | 114 | false | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables a... | \boxed{\lambda_{\min} = 32.2, \lambda_{\max} = 78.5} | ugphysics_SemiconductorPhysics | 118 | true | false |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{E_C-0.27} | ugphysics_SemiconductorPhysics | 131 | false | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \[
\boxed{\frac{e D_{\mathrm{p}} p_{n 0}}{L_{\mathrm{p}}}\left(e^{\frac{q V}{k_{\mathrm{B}} T}} - 1\right)}
\] | ugphysics_SemiconductorPhysics | 135 | false | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The problem has multiple answers, each of them should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represe... | \boxed{10^{20}, 2.745 \times 10^{11}, \frac{1}{3} \times 10^{12}, \frac{1}{3} \times 10^{12}} | ugphysics_SemiconductorPhysics | 140 | true | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{\theta(x-x_{0}) \frac{\sin((x-x_{0}) \sqrt{k^{2}-z^{2}})}{\sqrt{k^{2}-z^{2}}} e^{-(x-x_{0})z}} | ugphysics_SemiconductorPhysics | 142 | false | true |
The following is an open-ended problem from Semiconductor Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{1.83 \times 10^{13}} | ugphysics_SemiconductorPhysics | 143 | false | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be either True or False. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used... | \boxed{Yes} | ugphysics_Solid-StatePhysics | 16 | false | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \boxed{\frac{9}{16}} | ugphysics_Solid-StatePhysics | 29 | true | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \boxed{8.315 \times 10^{-16}} | ugphysics_Solid-StatePhysics | 65 | false | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{\left(- \infty, \frac{\pi^{2} \hbar^{2}}{4 m a^{2}}\right]} | ugphysics_Solid-StatePhysics | 102 | true | false |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and fo... | \boxed{1.457} | ugphysics_Solid-StatePhysics | 103 | false | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{E(k) = E_{0} - 2J(\cos k_{x} + \cos k_{y})} | ugphysics_Solid-StatePhysics | 109 | false | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{\omega=\sqrt{\frac{4 c_{1}}{m}} \sin \left(\frac{q_{1} a}{2}\right)} | ugphysics_Solid-StatePhysics | 131 | true | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and f... | \boxed{ 5.4, 1.48, 4.8, 1.8} | ugphysics_Solid-StatePhysics | 133 | true | false |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the s... | \boxed{m_{l} = \frac{m_{2}^{*2}}{m_{1}^{*}}} | ugphysics_Solid-StatePhysics | 134 | true | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \[
\boxed{q = n \frac{2 \pi}{a}, V_{0} = -\frac{2 A}{a}, V_{n} = -\frac{2 A}{a} \cos \left(n \frac{\pi b}{a}\right)}
\] | ugphysics_Solid-StatePhysics | 140 | true | false |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \[
\boxed{N k_{\mathrm{B}} \ln 2 - \frac{N}{2} k_{\mathrm{B}}\left[\ln \left(1-x^{2}\right) + x \ln \frac{1+x}{1-x}\right]}
\] | ugphysics_Solid-StatePhysics | 148 | false | true |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{\frac{\beta+\gamma}{2} \pm \frac{\sqrt{(\beta-\gamma)^{2}+4 |\alpha|^2}}{2}} | ugphysics_Solid-StatePhysics | 150 | true | false |
The following is an open-ended problem from Solid-State Physics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \(\boxed{\omega_{m} = \frac{\pi}{b} \sqrt{\frac{2(n-1) e^2}{M b}}}\) | ugphysics_Solid-StatePhysics | 152 | true | false |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and ... | \boxed{7.5} | ugphysics_StatisticalMechanics | 38 | true | true |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{\mu_{\mathrm{g}} = kT \ln \left[\left(2 \pi m k T\right)^{-3/2} \cdot \frac{N_{\mathrm{g}}}{V}\right]} | ugphysics_StatisticalMechanics | 41 | false | true |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{\chi_{\mathrm{mC}}=\frac{\mu_{\mathrm{m}}^{2}}{3 k T}} | ugphysics_StatisticalMechanics | 56 | false | true |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{\frac{3}{2n\mu_{0}}\left(1 - \frac{5}{12} \theta^{2}\right)} | ugphysics_StatisticalMechanics | 58 | true | false |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{k n \ln \frac{N}{n}} | ugphysics_StatisticalMechanics | 62 | true | false |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{-kT\left[\ln \frac{A}{N} + \ln \left(\frac{2 \pi m k T}{h^{2}}\right) + \frac{\varepsilon_{0}}{kT}\right]} | ugphysics_StatisticalMechanics | 65 | false | true |
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