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Einstein, in his 1905 relativity paper, allocates a section to the issue of reflection of light from a moving mirror and derives three formulas (angle, frequency, energy). What was his reason or motivation behind including this problem?
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Fluids can be characterized by the fact, that initially neighboring material fluid particles do not remain neighboring during the course of deformation.
The deformation gradient in continuum mechanics is defined via
$$\boldsymbol{F} = \dfrac{\partial \boldsymbol{\varphi}(\boldsymbol{X},t)}{\partial \boldsymbol{X}}$$
wh... |
In Peskin & Schroeder's Introduction to QFT problem 2.2a), we are asked to find the equations of motion of the complex scalar field starting from the Lagrangian density. I want to show that:
$$i\frac{\partial \pi^*}{\partial t}=\int d^3 x[\pi^*,H]. $$
So plugging the Hamiltonian in,
$$\int d^3 x[\pi^*,H]=\int d^3x [\pi... |
Based on previous q's and a's on this general topic, it seems there is little agreement on whether Mach's analysis is "correct". I am curious about actual experimental tests of a "closed Newton's bucket" in space. For example, if a thick, impervious and transparent sphere is filled with (say) 2/3's water and 1/3 air at... |
To describe a gauge theory on a topological nontrivial 3-manifold we need to consider a good cover of the manifold in contractible open sets with associated set of 3-connections:
$A=\{v_a,\lambda_{ab},n_{abc}\}$
where $v_a$ is related to the set $U_a$, $\lambda_{ab}$ to the intersection of two sets $U_a$ and $U_b$ and ... |
Lets consider a thermodynamic system at $T_1$ and a heat reservoir at $T_0$, where $T_1>T_0$.
The system cools down, i.e. it gives of heat to the heat reservoir (the heat reservoir can be thought of as the environment). The system, as it looses heat, has a negative entropy change. On the other hand, the heat reservoir ... |
I have a simple 2D Hamiltonian $H = \frac{k^2}{2m}$ and a square well. I assume $m = \frac{1}{2}$ so the Hamiltonian simplifies to $$H = k^2 = -\nabla^2$$When I solve the Schroedinger equation $H\psi = E\psi$, I would have thought the modes/eigenvectors would be $$\psi(x,y)\propto \sin(\frac{n_x\pi}{L}x)\sin(\frac{n_y\... |
An infinite wire carrying electrical current moving towards a stationary charge (perpendicular direction), why is there an electrical force on the charge in a direction parallel to the wire? I can only work out a force perpendicular to the wire, no parallel component. (Note in the wireframe, charge moves perpendicula... |
I am reading Einstein's book on relativity and ran into the relativistic rotating disc example, also known as Ehrenfest paradox. What is its resolution?
More specifically, imagine two identical rigid discs with 1m rods lining both their circumferences such that exactly $N$ rods suffice.
Imagine the two identical discs ... |
Imagine a manometer if one end is filled with fluid A and other with fluid B then why pressure at same level is not same?
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I'm struggling with the following problem:
Consider the semi-infinite potential well with equation:
$$ V(x) = \begin{cases} +\infty & x<0 \\ -V_0 & 0<x<a \\ 0 & x>a \end{cases}$$
Show, by solving TISE, that for $E<-V_0 \implies \psi(x)=0$ everywere. $-V_0 < 0$ and $a>0$.
Note: I know that $E$ cannot be less than the mi... |
Faraday's Law is of course:
$$\mathcal{E} = -\frac{d\Phi}{dt}$$
My contention is that the law should be written this way:
$$-\frac{d\Phi}{dt} \Rightarrow \mathcal{E}$$
In other words Faraday's law should be a conditional if then statement.
The reason is simple (I think?).
A misguided physics student might assert a cons... |
I am confused with the resolution of this question:
A system of two nucleons is in a state with a total isospin quantum number $T = 1$. What are the possible values for the total spin quantum number $S$ and orbital angular momentum $L$ for this system?
I know that $S$ is 0 or 1, but how can we know the $L$ without know... |
I am working on the mode expansion of the complex scalar field.
This previous question shows most of the relevant steps. In particular, I am interested in the second to last line.
I have plugged in $phi(x)$ and its conjugate and derivatives into the hamiltonian for the complex scalar field and have gotten to this expre... |
In Lagrangian formalism, we consider point transformations $Q_i=Q_i(q,t)$ because the Euler-Lagrange equation is covariant only under these transformations. Point transformations do not explicitly depend on $\dot{q}_i$ (except when we include change of time $t$). A point transformation that satisfies
$$L(Q,\dot{Q},t)=L... |
Say we have a box with a (large enough) side $L$ in which there is are $N$ indistinguishable particles, each having a speed $\vec{v}_i$. Let us also say these particles don't interact with eachother in any way but for elastic collisions (this, of course, also applies for when a particle bumps against a wall) and all of... |
Let $(M, g_{\mu\nu})$ be a globally hyperbolic spacetime and let $\Sigma$ be a spacelike Cauchy surface. The covariant Klein-Gordon equation has a well-posed initial value formulation, in the following sense: given any pair of smooth, compactly supported initial condition on $\Sigma$, $(\phi_{0}, \dot\phi_{0})$, there ... |
Considering that this is a meteorite that has broken through the Earth's atmosphere, what would happen to one struck by a meteorite? Not a large one of any sort, but one around the size of a fist. How fast are they moving when they land? Has this ever happened to anyone before? Obviously, the effects would be different... |
Cosmology textbooks and lecture notes often mention that there are two possible modes in the early Universe - adiabatic and isothermal, with the former affecting both the matter field and the radiation field, while the latter affecting only the matter field. However, these texts do not make it clear as to why there oug... |
In standard QFT, each term in the perturbative expansion for a gauge theory is not necessarily gauge-invariant. Only the whole sum of Feynman diagrams is guaranteed so.
However, at least for QED, there have been attempts to do the perturbative expansion solely in terms of gauge invariant quantities, cf. "QED : A Proof ... |
Would a static non movable parabolic solar collector always focus the light hitting such collector to the same position of its focus?..
Or it's focal position would vary depending on where the sun is hitting the collector?
|
Is it possible for a region of space in our universe to reenter an inflationary state? For example, if a particle accelerator collision of sufficiently high energy recreated conditions under which the early universe experienced inflation, would that patch of space inflate?
An argument in favor of it restarting is the n... |
Consider a slinky whose one end is fixed and the other is free. The textbook approach for analyzing its longitudinal vibrations is to use the wave equation along with Neumann's boundary condition, i.e. assume that at the free end the slinky is neither stretched nor compressed. However, this is easily violated by initia... |
Imagine Alice and Bob have two pairs of entangled particles, pair A, and pair B. Imagine they have agreed beforehand that pair A measurement preceding pair B measurement constitutes a bit with value 1 and pair B measurement preceding pair A measurement represents a 0 value bit. Would they not be able to use this predet... |
Does General Relativity imply greater accelerations than Newtonian gravity in strong gravitational fields, such as at 2 m/s^2?
Do the general relativistic corrections add up to more "gravity" in strong gravitational fields?
|
My understanding of a winter freeze breaking a pipe is that if you get an ice slug "somewhere" a few feet or more upstream of a closed faucet then any subsequent freezing will cause a pressure increase because of water expansion and that cracks the pipe.
So what happens if you have a vertical pipe and make the top of t... |
I have two iron bars in a vacuum of $10^{-7}$ Torr. One is highly magnetized and the other is not. Will outgassing from the magnetized bar be less than the outgassing from the non-magnetized bar? Essentially what I'm asking, will the magnetic forces in the magnetized bar prevent gaps from occurring in the bar due to ma... |
Is there some way to measure Lambda, the cosmological constant, independent of $H_o$,
the Hubble constant and omega_lambda, the Dark Energy density? A standard equation for calculating Lambda, adapted from its wikipedia entry is:
$$\Lambda=3\left(\frac{H_o}{c}\right)^2\Omega_\Lambda*l_{pl}^2$$
At this site, the value ... |
I am a high-school student working with CRT electron gun. I want to make a setup using a CRT gun of an old television set where the beam will hit a target metal. I am making this setup at my home. I want to ask if will it be harmful or if will it cause any damage to lifestyle or emit harmful radiation.
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I'm now trying to learn about Fracton. In the very early paper studying Majorana checkerboard model, it is claimed that the ground state degeneracy ${D_0}$ on ${L \times L \times L}$ 3-torus is ${log_2D_0 = 3L-3}$. Although this is proven nicely with algebraic representation, I don't have a good intuition in understand... |
I've heard people argue that decay rates in the past could have been faster. Despite not having a mechanism for this, I am curious about it. The oklo reactor is commonly cited as proof that decay rates have not changed, but I'm wondering if just changing the decay rates, say 20% for each type of decay, if the neutron f... |
I have atmospheric spectra given in W/m2/sr/nm units and wavelength in nm. I want to convert W/m2/sr/nm to kilo Rayleigh/nm (kR/nm) for any wavelength.
I tried the following method from this paper: https://opg.optica.org/ao/abstract.cfm?URI=ao-13-9-2160.
I also wanted to know what method I should use to get the brightn... |
For a thermodynamically isolated system, will it eventually move toward thermal equilibrium? Will there be exceptions to the system?
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If we have an aluminium vessel containing ice at 0 °C and we supply heat to it.
Will the ice first melt completely and then the temperature of the whole system increases or will the vessel's temperature increase simultaneously as the ice is melting?
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I was reading interesting article about possible life signs detection in exoplanets, where JWS telescope have captured that exoplanet K2-18 b atmosphere has Dimethyl sulfide traces. This chemical element in Earth is only produced biologically, mostly in seas/oceans by Phytoplankton, having some specific smell, hence,- ... |
First picture below is from last section of 23th chapter of Feynman's Lectures on physics. I don't understand the red line.
This section talks about resonance in nature. It was very interesting and I understood what transparency was all about. But in the last example, I don't understand why the sharp resonance corresp... |
I have a generic tight-binding Hamiltonian of the form
$$H=\sum_n A c_n^\dagger d_n+Bd_n^\dagger c_n +C c_{n+1}^\dagger d_n + D d_n^\dagger c_{n+1}$$
where $A,B,C,D$ are parameters (hopping amplitudes) and the system is a two-sublattice system, one sublattice for each of the operators $c$ and $d$. I would like to know ... |
Given that the correlation length diverges at the critical point, why are domains of finite size?
What is the relationship for a ferromagnet between correlation length and domain size?
|
I am a high school student writing a research paper on cantilever beams. I am investigating the relationship between the distance at which a fixed mass is placed on the beam and the time period of its oscillation. On a 100cm ruler, I made holes at regular intervals. Each time, I attached a (100g)mass to one of the hole... |
An observer, initially at rest in infinity, is radially infalling through a Schwarschild black hole of mass M. Also a photon is radially infalling, almost cathing up the observer at a radial distance $r_o$.
If the energy of the photon at infinity is $E = \hbar w_{\infty}$. What is the frequency w of the photon that th... |
I wish to solve the advection-diffusion equation for the concentration $c(x)$ at steady state inside a 2d circle, where the advection is only in one direction (along the x-axis).
The picture here below demonstrate the advection direction
I'm convinced that this problem can be narrowed down to a 1D equation
$$\frac{\pa... |
From Kerr metric, we do know that there exist a function with the form of:
$$\Delta = r^2 - 2 M r + a^2 \tag{1}.$$
Following $[1]$, I did understand the coordinate transformation from Boyer-Lindquist (BL) to Kerr-Schild (KS) coordinates, (BL$\to$ KS), for the Kerr spacetime:
$$
dt' = dt + \frac{2 M r}{r^2 - 2 M r + a^... |
I'm going through Mahan's book on Many Body Physics, and I'm a bit confused about one of his claims. First he expresses the position of an atom as
$$\textbf{R}=\textbf{R}_{i}^{(0)}+\textbf{Q}_i$$
where $\textbf{R}_{i}^{(0)}$ is the equilibrium position and $\textbf{Q}_i$ is the displacement from equilibrium. Based on... |
I'm currently Grade 11 and learning physics with the topic of oscillations, sadly my teacher didn't really give me a good understanding, besides a formula we have to memorize and just use mindlessly. My book sadly states that the formula derived is above the "standard of mathematics for my level". However I'm quite an ... |
my equation is a=10log_10(x/10^-12). I have the error value for a, but I'm struggling to propagate the error for x
|
Out of curiosity, I am interested in Lagrangian dynamical systems that can be expressed in a "linear" manner. By this, I mean that their Lagrangian can be expressed, quadratically, as
$$L = \frac{1}{2} \dot q^T M \dot q - \frac12 q^T K q^T,$$
where $q \in \mathbb{R}^n$; $M$ and $K$ are symmetric, positive-definite, $n$... |
In cylindrical coordinate, the stability for a cylindrical liquid column/ligament can be analysed using perturbation theory by applying small perturbation in radial direction as follow;
$$\rho(z,t)=\rho_0\epsilon e^{(\omega t+ikz)}$$
The physical meaning is quite clear as I can say I am applying small perturbation in r... |
The spectral radiance as discussed here is certainly correct, but I fail to apply it to my problem.
Problem: I want to calculate the SR of a gas (given temperature, density and target wavelength) and fail to understand why it does not depend on density.
Explanation: The radiation source can be viewed as a superposition... |
Are there any (famous?) periodic potential functions in 1d, $V(x) = V(x+L)$, so that the Schrödinger equation with periodic boundary conditions $\psi(x)= \psi(x+L)$ is exactly solvable?
I can do it if $V$ is piecewise constant...
|
A chain of $n$ links of mass $m$ is being pulled upwards by a force $F$.
Trying to study this system, here are my questions and thoughts:
Each link accelerates at a rate $\frac{F}{nm}$ (?)
What are the forces on each link? There is the mass of the link as well as the masses below it, but what about tension? It seems ... |
According to the most reliable source on the internet. Hydrogen has a density of 0.07099 Kg/L. Thus divided by it's molecular mass, in one liter of liquid hydrogen we should have 35.21888395 mol.
Suppose the same liquid hydrogen is kept in that same container without venting. Then allowed to reach standard room tempera... |
I'm currently tackling QFT in curved spacetimes for the first time, mainly using "Quantum fields in curved space" by Birrell and Preskill's notes on QFT in curved spaces, to get a general idea of the subject.
We know that, in a globally hyperbolic spacetime, the Cauchy problem for the Klein-Gordon field is well-posed, ... |
I have a question which I cannot intuitively understand. In many articles I saw a Sagnac loop being used to generate polarization entangled pairs of photons. The principle is rather simple - you split the pump beam into two beams with perpendicular polarization, which then propagate through Sagnac loop in two opposite ... |
Consider two point charges of equal charge Q and mass m seperated by a distance R in free vacuum. Both the charges are initially kept stationary despite the repulsive force between them.
After time t = 0, one of the charges is allowed to move while the other charge is still fixed in its original position.
As the mobile... |
Standing barionic waves in CMB require that the geometry - i.e. the spatial perimeter condition - does not change for a sufficiently long time. How long should the standing wave of a byryon oscillation be sustained to not be significantly affected by cosmological spatial expansion, and at the same time to provide the m... |
All derivations I have seen for the Fermi-Dirac statistics presuppose the grand canonical ensemble. However, all applications of it, e.g. ideal quantum gases, electrons in a metal and semiconductors, are assuming a system where $N$ is fixed.
Why can the Fermi-Dirac Statistics even be used, and what is the meaning of $\... |
I need your help with an issue about Dirac gamma matrices. Precisely, I need to know if $\gamma^0\gamma^\mu$ generates an irreducible representation of some algebra. This problem has come out in the following treatment. I was trying to find all internal symmetries for the Dirac fields of the lagrangian (c, d are number... |
What does instantaneous velocity mean?
on google it says "Instantaneous means something happens very quickly, in a single moment. It's similar to the meaning of "instant", but most English speakers would say that something that is instantaneous happens even more quickly", so why are we concerned with instant velocity o... |
Does the work done in dQ=dU+dW include just the external work done by the system (on the atmosphere given by pdV), OR does it also include internal work done in a system--be it conservative or non-conservative. An example of such internal work done is the following...take an isolated room with a container,gas and a pis... |
In the cosmological perturbation theory course per Hannu Kurki-Suonio (2022) : https://www.mv.helsinki.fi/home/hkurkisu/CosPer.pdf, there is a remark in the text page 5 that puzzles me. The text goes like this :
We write the metric of the perturbed (around FRW(0)) universe as $g_{\mu\nu} = \bar{g}_{\mu\nu}+\delta g_{\... |
I am trying to work through this problem so that I can understand how to convert from pressure values to radius values inside a planetary core in a code. The core has variable density depending on whether the radius is in a solid inner core region or in a liquid outer core.
I was able to obtain two different pressures ... |
Let's consider a case in which a bucket is revolving in a vertical plane with gravity acting on it. At the highest position the gravity is acting downward but water is not going downward. Is this due to centrifugal force?
|
I know the two-point function is given by:
$$
\Gamma^{A_\mu^a A_\nu^b}(p) = -i \delta^{ab} (g_{\mu \nu} p^2 - p_\mu p_\nu + \frac{1}{\zeta}n^\mu n^\nu)
$$
and I am looking to solve for the inverse of this $I_{\nu \rho}$:
$$
(g_{\mu \nu} p^2 - p_\mu p_\nu + \frac{1}{\zeta}n^\mu n^\nu)I_{\nu \rho} = g^\mu_\rho
$$
with $I... |
Virasoro minimal models are supposed to be solved, which is certainly true in the A-series and D-series, but the E-series models are more exotic. Do we at least know the (non-chiral) fusion rules? The more explicit the answer, the better!
|
I have seen anecdotal testing of fuel cell stacks. Intended to demonstrate that their power output can be improved through the addition of a centrifugal blower.
What are the limits associated with turbocharging a fuel cell stack?
Is fuel cell power output principally limited by fuel supply, or the stack itself?
|
I derive $E \times B$ drift $\vec v_{E \times B} = \dfrac{\vec E \times \vec B}{B^2}$ and in SI I use V/m and T for the fields. I do not use Gaussian (cgs) units often, but I thought this equation holds for cgs. However, the conversion factors for statvolt/cm and gauss are $1/3 \times 10^2$ and $10^4$, so one gets addi... |
Without getting into what happens at the center of a black hole, I think it's correct to describe objects that come close to the singularity as being propelled forward in time faster than those further from that singularity.
So - from the perspective of anything that's falling into a black hole at this moment (as I sit... |
I am currently following an introductory class on statistical mechanics. This course starts with general notions of statistics (as a reminder), goes over explaining why one would want a statistical description of the world by taking a look into the classical and quantum cases. Based on these various examples, the cours... |
How is the following gravitational time dilation formula from this Wikipedia article derived?
$$T_d(h) = \exp\left[\frac{1}{c^2}\int_0^h g(h') dh'\right]$$
where $T_d(h)$ is the ''total'' time dilation at a distant position $h$, $g(h)$ is the dependence of g-force on "height" $h$, $c$ is the speed of light.
|
Consider a spin Hamiltonian. I am interested in understanding how the spin-spin correlation function $C(r_{ij}) = \langle \boldsymbol{S}_i \cdot \boldsymbol{S}_j \rangle - \langle \boldsymbol{S}_i \rangle \langle \boldsymbol{S}_j \rangle$ relates to whether or not the system is gapped or gapless. Given the system is... |
We have an enclosed chamber filled with water. From the top of the chamber there is a metallic tube connecting the chamber to a monometer. We increase the pressure of the water inside the chamber buy pushing down with a plunger. There is airgap between the monometer and the water. Can the monometer show the pressure i... |
A while back I came across a problem in which I were to find the force of attraction between a magnetic dipole and a spherical iron ball (which is much smaller than the distance between the dipole and the centre of the ball).
The solution was pretty straight forward, I assumed that the field from the dipole magnetizes ... |
I understand that electrons moving in a conductor will generate photons by colliding with the conductor lattice and that this generates photons. What about Na+ or K+ ions in a salt solution, particularly when they are moving thru ion channels? What kind of particle (photon, boson?) is generated by this to create an E... |
I am in the beginning of my first Quantum Mechanics class, and I just learned about state vectors.
From my understanding, the representation in a basis is related to the probability distribution of the object being in one of the basis states when measured, i.e. writing a state vector in the position basis would tell yo... |
I read in textbooks that the mobility of electrons is affected by lattice scattering caused by vibrations of the lattice and by impurity scattering caused by impurities because they disturb the crystal's periodicity.
Both scattering mechanisms depend on temperature. The higher the temperature, the greater are vibration... |
We're all familiar with the typical diagrams of standing waves of a string, as in this image from Wikipedia:
The thing that bothers me is that they ignore the reality that the string is vibrating in three dimensions. If we say X is the longitudinal direction and Y is the up-down vibration, what about Z (vibration towa... |
The AdS/CFT correspondence conjectures a duality between a $(D+1)$ dimensional gravity theory in asymptotic AdS spacetime with a $D$ dimensional conformal field theory. Is there any sense in asking whether the 2D CFT on the string world-sheet could have a 3D gravity dual? Is it possible that the 2D string world-sheet i... |
This is from the intro to a problem 36.5 in Srednicki and not part of the problem itself. I am having trouble proving that $$\mathcal{L}=i\psi_j^\dagger\sigma^\mu\partial_\mu\psi_j$$
Has $U(N)$ symmetry. $j$ is to be understood as going from $1$ to $N$ and being summed over. Srednicki says to take the following transfo... |
Considering a set up where a conducting pendulum oscillates between two permanent magnets, I want to somehow calculate the power dissipated by the magnetic braking force the magnets provide, in order to predict the time it would take for the pendulum to loose it's energy and come to rest. I read some articles on Joule... |
I'm trying to use the Fourier transform method to solve the following PDE:
This is a an infinite string with a pulse for it's initial condition. (At $t=0$, the string is stricken sharply so that the impulse $\Delta J$ is transferred instantaneously at position $x=0$).
I wrote the PDE in terms of the Fourier Transform:... |
Consider the action integral, $S[\gamma] := \int L(\gamma(t),\dot{\gamma}(t),t)dt$. We can always re-write it in terms of an arbitrary curve parameter $\tau$ which need not coincide with time $t$: $$S[\gamma] = \int L(\gamma(\tau),\dot{\gamma}(\tau)/\dot{t}(\tau),t(\tau))\dot{t}d\tau $$ (In both formulae the overdot re... |
According to fundamental concept of thermal conduction, heat flows from higher temperature to lower temperature. As in Carnot cycle, there is isothermal expansion and compression as a process i.e. Temperature is constant. So how does heat is flowing from source to system or system to sink in Carnot cycle if Temperature... |
In the common treatment of the Thomas precession, there are three frames:
the rest frame of the nucleus
the instantaneous frame associated with the electron at the time t, having a velocity of v in the x direction.
the instantaneous frame associated with the electron at the time $t+\delta t$, having a velocity of v in... |
What is the amplitude and frequency of wave with the following wave equation:
$$y = A \sin^2(2(kx - \omega t))$$
I plotted the wave at $t = 0$. The resulting wave has amplitude $A$. But my textbook gives the answer as $A/2$.
|
I am following this paper here (arXiv here). What I want to do is derive equations ($2.7$) and ($2.8$) given in section $2$. While the authors include the higher order Euler Lagrangian terms in their derivation, I do not.
I understand the procedure the authors have followed - but if I attempt to derive the field equati... |
How do I convert spectral radiance $\rm W/m2/sr/nm$ to $\rm kR/nm$?
I tried the following method from this paper: https://opg.optica.org/ao/abstract.cfm?URI=ao-13-9-2160
|
A tuning fork of frequency 480 Hz is used to vibrate a sonometer wire having natural frequency 416 Hz. The wire will vibrate with what frequency?
My textbook gives the answer as 480Hz, but i don't understand how. I feel normal modes will set up in the wire. Maybe some superposition of the normal modes will result in wi... |
Imagine an astronaut spills boiling hot coffee inside the orbiting space station, where do the steam go? I mean the coffee will likely form into many many balls but they at still very hot!
|
I am looking into the $k\cdot p$ Hamiltonian approach to describe a semiconductor system. The simplest system appears to be the 2x2 system which can be visualised as: \begin{pmatrix}
\epsilon(k) && \frac{\hbar kP}{m_0} \\
\frac{\hbar kP}{m_0} && \epsilon(k)-E_0
\end{pmatrix}
this is for a two-band problem. Which I assu... |
In the answer to a question I previously asked, the following manipulation was done but I don’t understand it$.$
$$ (U_{jm}\psi_m)^\dagger=\psi_m^\dagger U_{mj}^\dagger $$
aside from the context from the original question, we don’t apriori know anything about $U$. Concretely, what I don’t understand is that typically w... |
I am currently learning about quantum mechanics in my 12th grade Physics course and we're currently covering nuclear energy levels.
I understand that alpha and gamma decay is discrete, as there is only one particle involved in the decay, however with beta decay, the energy, momentum, and mass is shared among the electr... |
I was reading this topic, and this is what I Found:
Consider a rod of length $L$ which is fixed between to rigid end separated at a distance $L$. Now, if the temperature of the rod is increased by $Δθ$, then the strain produced in the rod will be:
Thermal strain,$$ε = \frac{ΔL}{L}=\frac{\text{Final length - Original L... |
In a 1 dimensional infinite potential well with width $a$, the ground state wave-function is given by
$$\psi(x) = \sqrt{\frac{2}{a}}\sin(\frac{\pi}{a}x)$$
The action of the position operator in the position space is defined as
$$\hat{X}\psi(x) = x\psi(x)$$
Basically, in the case above, I would write
$$\phi(x) = x\psi(x... |
It is well know that scientific tools , eg bubble chamber, can keep track of particle trajectories. Now here is my doubt. Quantum mechanics, which is a statistical theory, says that trajectories do not exist, eg electrons do not describe defined orbits around the nucleus. So how quantum mechanics reconcile with the pre... |
I am currently thinking about the irreversibility paradox. I am not working in this area and my question is certainly not original but I couldn't see it stated in that form yet.
I can't grasp how are the trajectories of an Hamiltonian dynamic are organised in phase space. Consider a system such as an ideal gas. Here ar... |
Considering the curl of the electric field of an electric dipole, this will be zero in absence of magnetic effects which is clear to me. I watched a video by 3Blue1Brown (some time ago) who explained the curl of an electric field illustratively in terms of a vector field. Considering a point in the electric field of an... |
In my book, it explains why current can flow even if the channel ends:
The device still conducts: as illustrated in figure, once the electrons reach the end of the channel, they experience the high electric field in the depletion region surrounding the drain junction and are rapidly swept to the drain terminal.
I can'... |
What is the branch of physics that asks the question 'what was before the Big Bang', assuming the Big Bang is truly what happened at the beginning of the universe? If there could be a better model that describes the start/formation of the universe, then the equivalent question would be: What is the branch of physics th... |
I encountered this problem while working on this exercise. The question is to find an expression for the acceleration of the two blocks. I started with writing newtons second law for the two blocks and newtons second law involving torque which is related to the angular acceleration of the pulley. My question is: is th... |
In calculating the exit velocity of the water in a water rocket, all the sites I have found use Bernoulli's equation in the rockets frame of reference. I know that that is correct if the rocket was an inertial frame eg being held at rest or moving with a constant velocity. However the rocket is being accelerated or put... |
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