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If we have a ray striking a plane then the unit vector in direction of the incident ray can be thought of as rotating in a plane that contains the normal to interface and the part of the unit vector along the plane of the interface. However, I can not understand why this unit vector is not rotated around lines parallel...
In high school, I hear a lot about semiconductors. Semiconductors are used to make transistors and diodes. A semiconductor material has an electrical conductivity value falling between that of a conductor, such as metallic copper, and an insulator, such as glass. In my textbook, they say that its conducting properties ...
I have a question about the Gauss-Bonnet invariant $T$, \begin{equation} T=R_{\mu\nu\alpha\beta}R^{\mu\nu\alpha\beta}-4R_{\mu\nu}R^{\mu\nu}+R^2 \end{equation} It is known that $T$ is a topological invariant, which implies that it's an intrinsic property and does not contribute to the field equations in an least action ...
The first law says you can’t create energy. OK, but you can give energy to a ferromagnet and magnetize it. Then you can magnetize as many other ferromagnetic materials as you want, and not diminish the magnetic field of the first one you had. I don’t understand how there can be no loss and how that is not considered br...
I was taught that light tends to take the 'fastest' route. However, this made me wonder about the following scenario: Suppose the start and end point (source and observer) are at the edge of a large cube of one medium,inside it but very close to the edge. Surrounding the cube is a material through which light can trave...
For electrons in a periodic potential, the effective mass of an electron in an energy band can be positive or negative depending on its quantum state specified by $n,k$ i.e. its energy $E_n(k)$ and crystal momentum $\hbar k$ in the band or in short, where it lies in the band. This is because the effective mass is given...
I am currently studying out of Vibrations and Waves by AP French. I have been trying to solve this problem but seem to be having trouble deriving mathematical equations for it: I have a qualitative understand about certain parts of the question that I will explain shortly, but is there any law that I can use to relate...
I saw in my textbook that a field can only be conservative if it happens to be spherically symmetric. Why is this so? Is there a good proof for this?
Background info: My understanding: 1. Weyl transformation is a local rescaling of the metric tensor $$ g_{ab}\rightarrow e^{-2\omega(x)}g_{ab} $$ A theory invariant under this Weyl transformation is called conformally invariant, or Weyl invariance or with Weyl symmetry. Diffeomorphism maps to a theory under arbit...
Does anyone know the name of lab equipment that can generate specific high frequency currents (not radio/signal frequency)? Does anyone know the name of lab equipment that can generate specific high frequency currents? I need a AC voltage generator that can produce a current in the 1400 MHz frequency range that can be ...
I was doing a physics problem, and it had asked me to find the maximum $K_e$ loss, but I don’t understand why the loss is maxed when the objects stick together (the collision is inelastic).
So the Lorentz force on a massive particle is given by $f^{\mu} = qg^{\mu\alpha}F_{\alpha\beta}\hat{v}^{\beta}$, where $\hat{v}^{\beta}$ is the four vector of the particle and $F_{\alpha\beta} = \partial_{\alpha}A_{\beta}-\partial_{\beta}A_{\alpha}$ is the EM field strength tensor, with EM potential $A_{\alpha}$. I wan...
I have a vector rotating from some rotation matrix: $$\vec{r_1} = A \vec{r_0},$$ $$A^T \vec{r_1}= \vec{r_0}.$$ To find out how this changes in time: $$\dot{\vec{r_1}} =\dot{A} \vec{r_0} = \dot{A} A^T \vec{r_1}$$ Then, because $$A A^T =1$$ We have $$\dot{A} A^T + A \dot{A^T} =0$$. $$\dot{A} A^T = -A \dot{A^T} = -(\dot{A...
The question is, in short, where in the composite fermion argument are electron-electron interactions used? I know that interactions, namely Coulomb repulsion, between electrons are crucial in explaining the FQHE. Without them we simply fill the known single particle eigenstates and we are certain that at non integer f...
Suppose we want to make a drone fly on the Moon (the gravity on the Moon is 1/6 of that on Earth), only by making use of its rotors and air. The drone is as light as possible ($m_{min}(kg)$, has dimensions $l(m)$ long, $w(m)$ wide $h(m)$ high. The rotor blades have an as big as possible length of $r(m)$ (which is of co...
When reading about how we can use a mass spectrometer in order to determine the mass of atoms/ions, several books that I have considered say that a mass spectrometer allows for a measurement of the mass-to-charge ratio of ions. Moreover, it is stated that the mass can be determined if the charge is known, but there is ...
I have several magnifiers/magnifying-glasses of varying quality with either nothing inscribed on them, or power ratings that I think are wrong. How can the power of a magnifier be determined when no values are given? Kyle Downs at quora.com states: Magnification $M$ of a single lens is $M=\frac{f}{f-d}$ I don't know...
I am studying QFT. My question is as the title says. I have read Weinberg and Schwartz about this topic and I am still confused. I do understand the meanings of the words "Poincaré group", "representation", "unitary", and "irreducible", individually. But I am confused about what it means for it to "be" a particle. I'm ...
I think it diverges since we have $$g(p)\sim\int dp p^2\frac{1}{p}\sim p^2.$$ So do we need to regularize even a free theory?
How would you find the lorentz force on a current-carrying wire that is looped into a solenoid? As a followup question: How could one use the amount of force calculated to determine whether a wire will be able to hold to those forces.
Watching a visualization of Schrödinger’s equation, I noticed that the wave function for a 2-dimensional particle was placed in a 3-dimensional graph consisting of 2 Real axes and an Imaginary axis. Does the wave function for a 2D particle rotate through “imaginary space”, or could that third axis be substituted with t...
I have a question! I was learning about JJ Thomson's Cathode Ray Tube experiment and I understand why the ray goes up when it passes through a Wien's filter, but I cannot plenty understand why it goes down when a magnet its applied by the sides. In this picture for example when professor applies a magnetic force, the r...
So, I once watched a video (I think it was by Andrew Dotson) that I can't find any more about techniques used to deal with singularities in path integrals. The presenter mentioned how the integral formula: $$\int x^{n} \; \mathrm{d} x = \frac{1}{n+1}x^{n+1} + C$$ cannot be used for $n=-1$. However, to deal with the sin...
I was reading my textbook and I encountered a section where it explains that Centripetal Acceleration is not constant, thus, I wonder if jerk exists in Uniform Circular Motion? The textbook states that it happens due to the continuous change on the vector's direction. So, pretty much. Does jerk manifest? or, if it does...
Here, in page 11, you can see the so-called 'handbag' diagram that explains how a virtual photon emitted in a deep inelastic scattering (DIS) process interacts with a parton. I'm going to use this diagram to compute the amplitude of the process $\gamma P \rightarrow X$, with $P$ the proton and $X$ a set of undetermine...
Equation 1.1.31 in this picture. How did the author reach to this solution from equation of motion? would anyone please explain it to me. I tried to derive it but no luck.
Suppose a shell rested on a smooth surface fires a bullet horizontally ,generating some energy of explosion say E. I know that initially system(shell+bullet) has no energy. When the internal forces do some work , the system gets some kinetic energy . So, Winternal_forces = (KE)bullet + (KE)shell How do i relate the Exp...
I came across a question from I.E. Irodov's Physics book: A tall cylindrical vessel with gaseous nitrogen is located in a uniform gravitational field in which the free fall acceleration is equal to g. The temperature of the nitrogen varies along the height h so that its density is the same throughout the volume. What i...
I can't understand the following reasoning: It seems to me that Eqs. (3.16), (3.15), and (3.14) contradict the Lorentz transformation (3.13). It seems clear that (3.14) imply that $y$ and $x$ are changing, contradicting what (3.13) says.
The biophysics behind measuring systolic and diastolic blood pressure manually with a cuff and stethoscope is that Determine the approximate pressure it takes for the cuff to occlude the brachial artery completely (normally around 120mmHg) which is indicated by a lack of pulse in the radial artery. Deflate then reinf...
As we are waiting in the subway station, we will hear the rail screeching when the train is arriving. Is it because soundwaves travels faster in a solid substance than in air? or is it a compartment in the rail?
Is it possible to explain the form of Lagrangian $L=T-V$ and action principle in the following way? The force that acts on a mass particle is due to the potential $V(x)$. This force drives the particle to minimize its potential energy. We also know that the attraction is a negative form of potential energy. On the othe...
What are some good books on Condensed Matter physics that will be accessible after reading Messiah (both volumes)? With no prior background in Condensed Matter, and that explain concepts in an understandable manner.
I was reading about UV-C radiation for germicidal applications and thought about how easily it is blocked by most plastics/glass. My question is, is there a material that doesn't block the UV-C light, but carries/refracts it like those old fiber-optic toys? Thanks!
I'm trying to write up all the possible superposition states for 3 spin-1/2 particles (one spin-up, 2 spin-down). Lets denote $|\uparrow \rangle = |0\rangle, |\downarrow \rangle = |1\rangle$. Intuitively, the states in superposition should look something like: $$ |011\rangle\ \pm|101\rangle\ \pm|110\rangle\ $$ (normal...
If i have a quantum harmonic oscillator system, say, a Quantum Optics system or a crystal where i have some $\Psi$ in occupation number respresentation in energy eigenbasis. $$\Psi=|n_1 n_2 n_3...\gt $$ $n_1, n_2 ..$ may represent photons or phonons of energy $\hbar \omega_1 , \hbar \omega_2...$ What perturbation/exper...
I want to calculate the angular size of the largest region in causal contact at the moment of recombination (z = 1100) to our universe, so we have: $H_0 = 68$ (km/s)/Mpc, $\Omega_{m,0} = 0.31$, $\Omega_{\Lambda,0} = 0.69$ and $\Omega_{r,0}=9\times 10^{-5}$. I know that: $$ \theta = \frac{d_{hor}(t_{ls})}{d_A}$$ where $...
All textbooks say that the path difference is $2d \cos \theta$. But in my mind, by constructing triangles, I seem to get $2d/\cos \theta$ and intuitively I thought as angle increases, the path difference should also increase. And when angle is $90°$, path difference should be infinite. Think something is fundamentally...
I've read that old satellites slowly lose altitude when encountering the very thin atmosphere, and strangely enough they speed up. My theory is that the work done by the drag force is insignificant in comparison to the whole energy of the orbiter, $$ E = -\frac{GmM}{2r} $$ so it essentially pushes it to a lower orbit w...
Can anyone please explain to me the importance of thought experiments? How does one arrive at a conclusion in a thought experiment. Like for example, the electron through double slit experiment is a thought experiment right? So how do we know the conclusion of the experiment is right?
Why different gases give slightly different temperature at same pressure in a constant volume gas thermometer? My book says we should lower the amount of gas in the thermometer to get perfect result
I seem to have $\langle\varphi|\frac{d}{dt} \varphi\rangle=0$ for any ket $|\varphi\rangle$, which I doubt very much... For any quantum state $|\varphi\rangle$, we know it's normalized and therefore $\langle\varphi|\varphi\rangle = 1$. Now $$\frac{d}{dt} \langle\varphi|\varphi\rangle = 2\langle\varphi|\left(\frac{d}{dt...
If a truck of mass 100kg is moving with some velocity say 10m/s ( pls assume friction is negligible but still truck is moving)when suddenly an object of mass 10kg falls on it from above and stickes to it ,such that the object has 1m/s speed (say) in the downward direction when it was about touch the truck. Now t...
I have some difficulties trying to understand the viscosity term in the Rayleigh-Plesset equation: $$R\frac{d^2R}{dt^2} +\frac{3}{2}(\frac{dR}{dt})^2 + \frac{4\nu_L}{R}\frac{dR}{dt} +\frac{2\gamma}{\rho_LR} + \frac{\Delta P(t)}{R} = 0$$ This equation describes the change in the radius of a spherical bubble. The main th...
In DIS the Bjorken limit is given by the conditions: $Q^2 \rightarrow \infty$, $\nu \rightarrow \infty$ and $x=Q^2/(2M\nu)$ is finite, where $Q^2$ is the opposite of the transferred momentum, $M$ is the proton mass and $\nu$ is the transferred energy. In this limit, the structure functions of the nucleons are functions...
What seems to incredibly bother me is why Gauss's law applies to any shape of a closed surface. Moreover, the fact that the electric flux is proportional to the enclosed charge is by many sources simply proven by using a point particle that is enclosed by a sphere. Hence the electric flux is proportional to the enclose...
$$\text{pressure} = \frac{\text{force}}{\text{area}}$$ Does pressure in this equation refer to the gauge pressure or absolute pressure?
It's very clear why the water gets thinner as it gets down. But in this picture attached, where the faucet nozzle is a flat slit, I do observe the water gets thinner and again wider after some point (making some 'X' shape) and further more I barely see the water flow has spun (rotated) a little. I don't know if this pi...
Why do we sometimes refer to the solar wind as young solar wind? What does young imply?
For example, questions like the following one- A square threaded screw of mean diameter 0.04 m and pitch 0.0025 m is used to lift a mass of 1 ton by a horizontal force applied at the circumference of the screw. What is the magnitude of the force if coefficient of friction is 0.06? Do not solve the problem but instead e...
Wigner's friend thought experiment mentions that there is an apparent paradox - 'when exactly did the collapse occur?'. Whether it occurred when the friend made the measurement, or when Wigner asked about it. Why is it different than if I flipped a coin and observed the result, but hid the result from my friend and so ...
Consider a circular loop of wire fixed on the rim of a wheel. This wire carries a current 'i' in it. When the wheel is at rest, which basically means that the current carrying loop is at rest, the magnitude of magnetic field at the center is, say B1. If I set the wheel in motion with a constant angular velocity with th...
Suppose I measure the same quantity twice with two methods, first I get 0 with 0.001 uncertainty, then I get 1 with 0.000001 uncertainty. We can see from this most likely there is something wrong with the uncertainties or measurements. I am faced with such a problem, I have multiple measurements of the same quantity wi...
Suppose we have a system that has discrete energy levels (e.g. hydrogen atom, potential well) and the stationary solutions for the wave function are $\psi_n$. I would assume that there should be a way in which one can model the transition $2\rightarrow 1$ by using as initial condition the stationary state $\psi_2$ for ...
It is well known that Einstein Theory of General Relativity has pathological solutions, called black holes, where the theory fails at some point and gives us infinite values. In order to solve this problems, there exists UV extensions of General Relativity. These kind of theories try to solve the singularity problem, a...
In LC circuit, we know that there will be charge oscillations, so emw will be produced. I just want to know emw will originate from where? Will it originate from within the capacitor? Or will it originate from the wires? (Like EM waves due to AC source.)
Please I am a learner don't Mark the question as downvoted one. My question is Is there any examples other than 'charged particle in magnetic field' which go in spiral path when gain some energy during the course. Here is the description In a cyclotron the charged particle moves spirally just because it gains some ener...
I have kinda formalistic question. Eg. we have normal symmetric chair with 4 legs, and mass $M$. Can we calculate forces of chair legs on floor surface $F_1,F_2,F_3,F_4$ with only this data and why not. How does the assumption, that chair is completely rigid or that it is elastic affect the problem. Is such calculation...
In basic atomic physics of light-matter interaction, very often we assume the atom is quantum mechanical with quantized atomic levels but assume the electromagnetic field to be a classical wave. It is true that this cannot explain the phenomenon of spontaneous emission and many other effects but is this framework mathe...
In nuclear fusion, the graph of reactivity is shown as below. How can we explain that by increasing the temperature after a certain value, the reactivity decreases?
I think that the answer is no, but in some sense it feels counter intuitive so I just wanted to check here. So if I understand it correctly, the General theory of relativity tells us that any sufficiently small object in orbit around Earth (that does not "experience" any forces) essentially follows a straight line thro...
Surface charge density of a conductor at a particular region on its surface is inversely proportional to the radius of curvature at that region. But this is valid only when there is no electric field. How will we calculate if electric field is also present? Please explain with any example.
It is known that Finite dimensional irreducible representations of Lorentz group can be indexed by two half integers $(s_1,s_2)$ and the sum $s_1+s_2$ is called the spin. Infinite dimensional unitary irreducible representations of (the universal cover of) Poincare group can be indexed by two numbers $m$ and $s$, while...
The Green function for Laplace's equation in three dimensions for a source at the origin is $$ \nabla^2 G(\mathbf{r})= \delta(\mathbf{r}) =\delta(x)\delta(y)\delta(z) $$ where is $\mathbf{r}=\mathbf{x}+\mathbf{y}+\mathbf{z}$ is the position vector. The solution is $$ G(\mathbf{r})=\frac{-1}{4\pi r}$$ where $r=\sqrt{x^...
I love to play with laser diodes and they have always been a fascinating thing for me. Usually, I play with $0.1$mW laser diode pointer (Which are just toys) . From some physics textbooks and videos , I learned a little bit about how lasing works , But I still wanted to know How a laser diode is made (meaning a teardow...
I'm reading some notes on the Anderson Hamiltonian: $$ H=\sum h_i c_i^\dagger c_i -q\sum_{\langle i,j\rangle}(c_i^\dagger c_j+c_j^\dagger c_i)$$ Where the $c_i/c_i^\dagger$ are fermionic annihilation/creation (ladder) operators. The notes say Since $H$ commutes with $N=\sum_i c_i^\dagger c_i$, it conserves the number ...
Imagine a structure exposed to wind. It is designed chemically so that a molecule striking the surface can transfer kinetic energy to electrons that are promoted to a higher energy state. These move through a conduction band and are collected as in a solar cell. Maybe a layered structure akin to graphite cut diagona...
Since I started quantum field theory I had very big issues with signs, especially when I had to pass from a tridimensional euclidean space to a flat four-dimensionale spacetime, with Minkowski metric. I read a lot of questions on this site trying to find an answer, but I could just walk around the problem without being...
Reading the book "Supergravity" from Freedman & van Proeyen I stumbled over the assertion that in 3D GR the vacuum solution $R_{\mu\nu} =0$ leads to a vanishing 4-rank curvature tensor $R_{\mu\nu\rho\sigma}=0$, therefore there are no gauge invariant degrees of freedom in the 3D GR vacuum case (I indeed found in Landau ...
I'm working through "Advanced Quantum Mechanics" by Franz Schwabl, and he uses this G-correlation function to estimate the first order correction to the ground state energy in a Coulomb system (section 2.2.3). In the course of doing so, he runs into the following expectation value (where the implicit state is the fille...
Why is the energy function $h = \dot{q_i}\frac{\partial L}{\partial \dot{q_i}} - L $ not always equal to total energy $E = T + V$? Here $T$ is Kinetic Energy and $V$ is Potential Energy. I've read that $h$ is not always the same as total energy for any given Lagrangian System, but I do not understand why this is. Unde...
Suppose we define a unit vector $\vec r$ along radial direction for a particle in uniform circular motion at an angular frequency $\omega$. Then we can write: $$\vec r = \cos(\omega t)\hat i + \sin(\omega t)\hat j$$ And the modulus of this vector is one. If we differentiate this to get the velocity we get: $$\vec v = \...
My professor has stated that the electric field inside a conductor is 0.I understand this However, he has also said that even if the conductor has some hole in it, the electric field inside this hole is also 0 Now, two examples which confuse me: Consider a thick spherical shell with radiuses $a,b$. Now, let there be a ...
I was looking for the exact theoretical value for specific heat capacity of copper. I found some telling 377, 385, 386, 390 J/kgK ... And for different room temperatures, 20 and 25 degree celsius, it shows different values on different websites. So my question is "Does the value of specific heat capacity of a material ...
On page no. $166$ of "Many-body quantum theory in condensed matter physics" by Henrik Bruus & Karsten Flensberg, while explaining the summation of Matsubara frequency, the following calculation is made : $ Res_{\substack{z=ik_n}}[n_F (z)]=lim_{\substack{z \rightarrow ik_n}} \frac{(z-ik_n)}{\exp {(\beta z)} +1}=lim \sub...
We are taught that only charged particles have an electric field in their vicinity and a neutral object does not. But a dipole is neutral overall and still produces an electric field. Why?
I was reading the book: 'Fundamentals of Physics by Halliday, Resnick and Walker', and in its 'Photons and matter waves' Chapter they discuss about the interactions of photons with electrons. Specifically in the discussion of Compton Effect, they explicitly used the law of conservation of momentum for the electron-phot...
I was looking at some calculations of the deflection of light by the sun. However, there is something that I cannot understand. They usually express a relation $$r = \dfrac{p}{1+e\cos(\theta)} \qquad (\star) $$ as if it were massive, knowing that nothing in this expression depends on the mass (but it depends on the mas...
The notion of renormalization is probably one of the most difficult to understand and bizarre properties of the QFT. As for the renormalisation of couplings it seems strange, from the first sight, that the coupling constants in the bare Lagrangian of interacting theory mostly have to be infinite in order to get a finit...
Imagine this sphere to rotate about its diameter, from the centre to the point of surface if we take all of them have equal distance that is 'r(radius of the sphere)'.So same linear speed right? I looked up many sites but they all say "The linear speed v = ɷr. That means the particles at different r will have different...
I have been reading about Molecular Orbital Theory for Chemistry. I tend to believe that when two Hydrogen atoms approach each other, whether the $1s$ orbitals are in-phase or out-phase is a random phenomenon. However I know that this is not so. Please provide some arguments to counter it. Please try not to indulge ...
If we consider the magnetization for paramagnetic materials, then we obtain $$M = -n\frac{\partial F}{\partial B} \propto B_J(x),$$ where $$x \equiv g\left( JLS\right) \cdot J \cdot \frac{\mu_B\cdot B}{k_B T}$$ is an auxiliary variable and $B_J( \ . )$ the Brillouin function. Now, what exactly is $J$ in this context? I...
I have been going through a number of articles to understand quantum circuits.I am trying to understand how a qubit gets coupled with the photons? But I am only getting answers of how a qubit gets coupled with a resonator cavity? Does both of these are the same?
Why do we use commutation relations when quantizing any system? In the case of developing quantum mechanics from classical mechanics, we write the hamiltonian and then quantize it by having the conjugate variable/observables obey the commutation relation. And this process is valid for any quantum system. The same is th...
I do not know of any specific other information needed to answer the question.
My question is closely related to this and this questions. However, instead of asking about the commutation relation between the operators, I would like to ask about their action of the Fock states. For definiteness, let's assume that we have two relativistic fermionic fields of different species whose annihilation ope...
As a specific example, consider a needle on a torsionless thread lowered from deep space over a rotating planet's pole. The needle will spin at a specified rate (based on elevation, planet inertia and planet roational speed). It seems like the needle in the space-time warp model would come to speed instantly (no acce...
Estimate the molar heat capacity of gadolinium at room temperature, given it's Debye temperature $155 \ K$. $C=2.4\pi^4 N_A k \left(\frac{T}{T_D} \right)^3\approx13000\ \frac{J}{molK}$. I didn't think this would work because this isn't supposed to apply to solid metals. Molar heat capacity of gadolinium is about $37\ \...
I was wondering about the nature of the 3 slit interference pattern, as shown in fig 1. The line labelled LT/2, matches with fig 2 and all other diagrams I have seen depicting the same thing. I was wondering about the line labelled LT/4, what are the conditions for this alternative pattern, given a set source wavelengt...
The goal. Calculate the partition function of the following systems: A gas of $N$ non-interacting distinguishable particles with non-degenerate energy levels $E_0=0$ and $E_1=\epsilon$; A chain of $N$ sites that can be either open ($E=\epsilon>0$) or closed ($E=0$) such that if the $i$-th element is open, then all ele...
My textbook stated that the degeneracy level of the hydrogen atom for $n=3$ is $18$. I'm trying to figure out why it's true. I'm familiar with the Bohr's module but I can't seem to figure out how to does it help me to calculate it. Is there a closed formula to calculate the degeneracy level of the hydrogen atom? If it...
$$I\propto \frac{\sin^2(N\delta)}{\sin^2(\delta)}$$ Where $N$ is the number of slits and $\delta$ contains the angle, wavelength and slit spacing dependence. In the limit as $\delta \to 0, I \to N^2$. This makes sense because as $N$ increases the sharpness of the maxima increases and therefore we expect that the intens...
Assume there are two conducting infinite plates. They make up a capacitor - one plate has a charge density of $\sigma$ and the other has a charge density of $-\sigma$. Assume the charges on them are constant. Now, assume that in some point a conducting block is inserted inside ( infinite in two dimensions as they were ...
When we get a minor static electric shock, we often hear a noise associated with the shock. Or for example, when you swat a fly with a zapper, you can hear a noise from the electric transfer. What causes this noise?
So, I have been watching some science videos regarding Einstein's theory on general relativity and until today the predictions based on his equations have been proven to stand. My question would be: what happens in the scientific community if one experiment proves it wrong (not only Einstein, but even other laws and th...
In this paper1 the following bandstructure of Bi$_2$Se$_3$ is shown: In "a" they show the bands without Spin orbit coupling (SOC) and in "b" they include SOC. It is said that: "Figure 2a and b show the band structure of Bi$_2$Se$_3$ without and with SOC, respectively. By comparing the two figure parts, one can see cle...
I'm reading a paper called: "A Simple Introduction to Particle Physics Part I - Foundations and the Standard Model" and i have some questions regarding the derivation of the raising and the lowering operators of $SU(2)$. in the adjoint representation for $j=1$ the only Cantan generator is the the $J^3$ matrix, so the r...
I've been going through the various sections of my Engineering Dynamics HW and I've been struggling to solve this problem for a while: A car is travelling at a speed of 30 m/s at the top of a hill at a given instant. The coefficient of kinetic friction between the tyres and the road is 0.8. The instantaneous radius of...
Is there any intuitive explanation of why resistivity of metal goes as $T^5$ at low temperature? The Debye theory gives that the phonon distribution goes as $n(\omega)\sim T $ at higher temperature and $n(\omega)\sim T^3$ at low temperature? What is responsible for this extra $T^2$ suppression? Also, how do I go about ...
Surface charge density of a conductor at a particular region on its surface is inversely proportional to the radius of curvature at that region. But this is valid only when there is no external electric field. How will we calculate if external electric field is also present? Please explain with any example. I think I h...