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As far as I know, a electromagnetic field can be generated by a variable magnetic field. The other thing I know is that, before the Bohr Hydrogen atom, the problem related to electrons around nuclei was that an electron rotating around a nucleus should have lost energy through radiation. Since the magnetic field produc...
If we take the movement of a rotating gyroscope held horizontally at one end with a rope, then the rotational momentum of the gyroscope's spin exists, as well as the rotational momentum caused by torque applied by gravity over time. This would lead to a linear combination of those rotational momenta, which would requir...
In the classroom my teacher stated that the Gauge-fixing term in the action $$\frac{1}{2\alpha}\int d^4x (\partial_\mu A^\mu(x))^2$$ transforms under $A_\mu(x) \rightarrow A_\mu(x)+\partial_\mu \theta(x)$ as: $$\frac{1}{\alpha}\int d^4x(\partial_\mu A^\mu(x))(\partial_\nu \partial^\nu \theta(x))$$ when inserting the t...
Consider an EM field $(\vec{E}(\vec{r},t),\vec{B}(\vec{r},t))$. I would like to determine the spectral irradiance ($\mathrm{W}/\mathrm{m}^2/\mathrm{Hz}$) of a surface receiving the field. According to Wikipedia, it is defined as $E_{e,\nu}(\vec{r},\nu)=\dfrac{\partial\langle\vec{S}\rangle}{\partial\nu}(\vec{r},\nu)\ve...
If a bulb is marked at 100W and 200V, we know that the bulb utilises a power of 100W when connected to a 200V potential difference. So, can we say that the bulb, when connected to twice the potential difference the bulb utilises a power of X watts?
Suppose I have 2 lemons each with a zinc nail and a penny for electrodes and I wire them up in series so that Nail-A passes through a load and connects to Penny-B and Nail-B connects to Penny-A. I think I understand that the lemon juice puts electrons into Nail-A as it creates zinc oxide and Penny-B is losing electrons...
I am starting to read "General Relativity" by Robert Wald. A little bit of my physics background: I am pursuing a mathematics major and I have not taken any physics courses, just Analysis and Differential Geometry. My doubt is mainly about the definition of manifold that the author states. His definition is similar to...
Looking for a database of spectral data in the ultraviolet to visible range (interested in roughly 200 to 800 nm) for common materials found in homes, vehicles, mass transportation, factories, etc. In other words, things like various cloth types, various metals, plastics, etc. There are a number of spectral databases ...
We consider a linear chain of atom connected by springs with constant $K$. We have the usual elastic force and we add damping force such that the dispersion relation is: $$ \omega = 2\sqrt \frac K m \sin \left(\frac {qa} 2\right) - \frac{i\Gamma}{2m} $$ I don't know if the expression correct, but for $\Gamma=0$ we fall...
This is just a thought experiment before someone mentions the cosmic censorship conjecture. If physicists are discussing it in papers and scholarship, I wanna see some of those theoretical angles too lol. So, If you took a black hole and turned it into a naked singularity, would the naked singularity have the same grav...
I quite often see papers considering a $\phi^4$ theory in three spacetime dimensions, but rarely do I see papers with $\phi^3$ terms. I understand that these kinds of interactions terms can have problems, but they can be defined sensibly in 4 dimensions by considering so-called bi-adjoint scalar fields, where each fiel...
I would like to understand Gauss' law for the electric field without using the divergence theorem. I'm already aware of related questions like this. Consider a charge $q$ placed in the origin and a box as Gaussian surface defined as: $$V = \{(x,y,z) : x \in [-a, a], y \in [b, c], z \in [-d, d]\},$$ with $a>0$, $c > b >...
I am trying to numerically compute the Berry Curvature for a generic quadratic Bosonic Hamiltonian of the form $$H = \sum_{ij} A_{ij} b_{i}^\dagger b_j + \frac{1}{2} \sum_{ij}\left( B_{ij} b_i b_j + \text{H.c.}\right).$$ After an appriate Fourier transform and Bogoliubov transformation, the Hamiltonian for the $n^{th}$...
The Einstein equations can be written as (here I am following the notation of Wald, Robert, General Relativity, Chicago, Chicago University Press, 1985) \begin{equation} \partial_{\alpha}\Gamma^{\alpha}_{\mu\nu} - \partial_{\mu}\Gamma^{\alpha}_{\nu\alpha} + \Gamma^{\alpha}_{\mu\nu}\Gamma^{\beta}_{\alpha\beta} -...
De Broglie theory of matter waves stipulates that the frequency increases with the weight of the object. However I believe there is no physical definition of an "object", it's an arbitrary category. We generally consider that an object is the sum of its parts: Let's take nunchucks for example, how do you move from the ...
I am trying to understand the following definition of matrix Lie group: A matrix Lie group is a subgroup $G$ of a $\operatorname{GL}(n;\mathbb{C})$ such that if $A_m$ is any sequence of matrices in $G$ and $A_m$ converges to some matrix $A$, then either $A$ is in $G$ or $A$ is not invertibile. Consider that the set o...
Let's consider a point-charge $q$ located in the origin, generating the following potential in cylindrical coordinates \begin{equation} \Phi(\rho,\varphi,z)=\frac{q}{\rho^2 + z^2} \end{equation} The problem is how to write it as an expansion of Bessel functions. I thought the Hankel transform could work, as $\left\lbra...
I am trying to get a better gras of Lie groups and Lie algebras and I was wondering if there's any book or general resource with problems and solutions in order to learn through practice.
For vehicles on "treadmills", how is the ground simulated by the drum (as depicted) to accurately represent the energy loss to drag. I have been conceptualizing the process below, but am skeptical of the results. $F_{drag}$ is the force equivalent to drag and wheel resistance acting on the vehicle as a function of ...
In my GR lecture I was given the following equation for the spacetime interval (signature $(+,-,-,-)$): $$ ds^2=(1+\frac{2\phi}{c^2})c^2 \, dt^2-(1-\frac{2\phi}{c^2})\delta_{ij}\, dx^{i}dx^{j} \tag{1}$$ I'm having trouble understanding what it means physically. I would suggest it means that the interval between two eve...
Say a force is doing work on an object in one dimension. I could calculate the average force over the distance with $$\frac{1}{\Delta{x}}\int_{x_1}^{x_2} F(x) \text dx$$ If I also formulated force as a function of $t$, I could calculate the average force over the total time period with $$ \frac{1}{\Delta{t}} \left| \in...
I am a self learner in quantum opitcs and the books they usually use the words like "single mode" and "multimodes". My question is what is a mode in electromagnetic theory ?
My instructor presented the following problem on capacitors: Plates 1, 2, 3, and 4 form two parallel plate capacitors as shown. Plates 1 and 2 are charged, plates 3 and 4 are not. Both pairs of plates are separated by distance d. Describe what you think would happen if you connected plate 3 to plate 2 with a wire. ...
Is there a word for the level at which a bottle needs to be filled such that if even a drop of additional liquid were in that bottle and that bottle were placed on its side on a perfectly horizontal surface with its lid removed then that additional drop of liquid will spill out. If that additional drop were not put int...
Is there a way to calculate the amount of electrons in a plate of a certain material and certain dimensions? What I want to know is how many electrons are available to remove from a plate when light of appropriate wavelength hits the plate(photoelectric effect).
Assuming we have a uniformly polarized sphere. Why does it happen that it exerts an electric field outside, but with a sphere polarized with some radial polarization the electric field outside is 0? Is it because in the second instance one can use Gauss law because of the radial symmetry, while in the first instance we...
In a multivariable calculus exam I took many years ago, one problem gave us a certain vector field ${\bf F}$ on $\Bbb R^3$, first asked us to show that ${\rm div}({\bf F})=0$, and then to find ${\bf G}$ such that ${\rm curl}({\bf G})={\bf F}$. I argued that since any two fields with the same curl must differ by a gradi...
I'm studying articles about spinning drop method. In most of approaches, the fluid movements are taken as rigid body rotation. My question is not about only spinning drop device, I want to know, when in nature do we have rigid body rotations for fluids. Should our fluids have large viscosity to considered rigid body ro...
I was reading a paper in which the authors use the operator of the form $\hat{A}\hat{B}+\hat{B}\hat{A}$ and it is implied to be experimentally realisable. (i.e either creating an apparatus to measure this operator or/and using some method to calculate the expectation value) My question is about how in general this o...
I want to understand which of the following possible decay modes for the B$^+$ meson is most probable: $$ B^+ \rightarrow \tau^+\upsilon_\tau $$ $$ B^+ \rightarrow \mu^+\upsilon_\mu $$ $$ B^+ \rightarrow e^+\upsilon_e $$ I think that it would be the electron as this is a fundamental particle and has the least mass, but...
My question comes directly from Section 7 of Srednicki's QFT textbook. I'm not able to reproduce Equation (7.5): $$\begin{aligned} [\cdots]=\frac{1}{2} \int_{-\infty}^{+\infty} \frac{d E}{2 \pi} \frac{d E^{\prime}}{2 \pi} e^{-i\left(E+E^{\prime}\right) t}[&\left(-(1+i \epsilon) E E^{\prime}-(1-i \epsilon) \omega^{2}\r...
Supose we have a charge $+q$ which is held at a distance $d$ from the plane $z=0$ not grounded. Very similar to the classic case: Electric induction in a grounded plane conductor But the infinite plane is not grounded. Which would be the charge distribution in the plane then? I assume that the charge conservation will ...
I have been working through some lecture notes and am quite confused on something. I am trying to understand how to average a quantity over an orbit (Keplerian) but I am struggling to get a clear idea on this. The notes I am using is: http://www.sns.ias.edu/sites/default/files/isima1.pdf So I am trying to do the exerci...
The definition that was given to me by my professor said that a Lifschitz transition is when the topology of the Fermi surface changes. For example, if we have a one-dimensional Fermi surface, we would have some curve $E_\lambda(k)$ where $k$ ranges over the Brillouin zone and $\lambda$ is some real-valued parameter. I...
Working on a estimation problem and we've been asked to estimate the height of the Earth's atmosphere given its mass is $10^{19}\mathrm{kg}$ and we must assume the density is $1\mathrm{\frac{{kg}}{m^3}}$ Stuck on where to begin with this.
For an multibody system with N point particles, in Newtonian frame, to solve for the N positions of each particle as a function of time: There is 1 equation for the center of mass. There are $\frac{N(N-1)}{2}$ force functions between each pair of particles. So there are $\frac{N(N-1)}{2} + 1$ constraint equations for...
Given that they can reach terrifying energies and temperatures, why isn’t fusion of protons a concern? After all, they start with a plasma and ram protons into each other. At some point the strong force will overcome the proton-proton electric repulsion, no? And as a corollary, can they re-purpose CERN to become a fus...
For electromagnetic induction, Lenz's law states that "the current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion." When we want to find the direction of this 'mechanical force', we use Fleming's Left Hand Rule...
Space after the big bang occurred have expanded dramatically. However at the same time the big bang happened it started to expand from that moment so what can we find before that point. For example, if we went back to the point where big bang happened what can we see? what is the point before it? is it nothingness?
We have a scalar field propagator in minkowski space with signature $(+,-,-,-)$ as $$ G (k)={1\over k^2-m^2 }.$$ But in Euclidean space the scalar field propagator is $$G (k)={1\over k^2+m^2 }.$$ Can anyone please explain how this conversion happen?
I was reading splitting of spectral lines in magnetic field and my book says In anomalous Zeeman Effect, Classically, the ratio of orbital angular moment to angular momentum $|\vec{L}|$ gives us $\vec{\mu_L} =\frac{e}{2m}\vec{|L|}$ and the ratio of spin angular moment to spin momentum $|\vec{S}|$ we have $\vec{\mu_S}...
I am currently reading Taylor's "Classical Mechanics", specifically the angular momentum chapter. In his definition of the conservation of angular momentum, Taylor states: If the net external torque on an N particle system is 0, the system's total angular momentum $\vec{L} = \sum \vec{r}_\alpha \times \vec{p}_\alpha$ ...
I am speaking about operators representing physical observables and am not interested in purely mathematical objects (if that's relevant to answering the question). I know that a degenerate eigenvalue corresponds to an eigenspace with dim > 1, which means 'linearly independent' eigenkets, even orthogonal eigenkets, tha...
Space is expanding, and this effect can be only detected at large scales, on the scale of galaxies and larger. If space is expanding, the expression $1/r^2$ for the law of gravity will be modified. How would this occur? I am phrasing the question as simply as possible on purpose. In detail, the first part of the questi...
Usually, an optical waveguide is considered in the following way. We have a plane wave traveling inside the waveguide at a certain angle $\alpha$ (which corresponds to the direction of the wavevector $k$). It gets reflected twice from the lower and upper boundaries of the waveguide. Then this reflected wave should have...
This is not a homework question or anything. I have finished schools and I always wondered why in physics exercises you can neglect the effect of air drag for example in case of basketball and I haven't found any precise explanation to this. I have figured out that the air drag is almost negligible in the situation whe...
If a fan moves the air and thus adds energy to the room, shouldn't the temperature go up, not down?
I have two questions regarding the $u$-channel in Feynman diagrams. $\textbf{Question 1:}$ Suppose I have a $\gamma\gamma\to\bar{\nu}_{\mu}\nu_{\mu}.$ One of the diagrams will look as one of the following: Is there a difference between these two? Are both allowed? If so, which is the correct one? $\textbf{Question 2:}$...
I was reading 'Welcome to The Universe', where in the appendix is a situation in which a hard disk, 7.5 cm in diameter, stores more and more information, before eventually becoming a black hole. Similarly, the amount of information we use is exponentially increasing in our world. So, if in the future, we develop comput...
Suppose I have two ice cubes and I want to stick them without any external material. Can I achieve this by keeping both on one another and extract some more energy from them ( by placing them in freezer) ?? I just want to know the answer ( in yes or no ) ??
Coherent states for a one-dimensional harmonic oscillator are given by: $$|\alpha\rangle = e^{-|\alpha|^{2}/2}\sum_{n=0}^{\infty}\frac{\alpha^{n}}{\sqrt{n!}}|n\rangle$$ ** ($|n\rangle$ is an eigen state of the harmonic oscillator) Books typically demonstrate the process for finding the uncertainty in position $\Delta ...
When a disk is in pure rolling, can the energy be conserved? And if the disk is in pure rolling on the inclined plane, there is static friction acting on the disk then how can the energy be conserved there?
Given the metric in AdS space $$ ds^2=\frac{r^2}{L^2}(-dt^2+d\vec{x}^2)+\frac{L^2}{r^2}dr^2 $$ I am trying to calculate the variation of the action of the KG equation in this metric. What would be the determinant of the induced boundary metric on the AdS space $\sqrt{-h}$? Also what would be the normal vector field $n^...
In a transformer, If the circuit of the secondary coil is opened, then the emf of the source equals the induced emf by self induction in primary coil So what makes them equal? Is there a law that proves that or is it based on experiment or something like that?
As a sanity check, I have tried to evaluate a Feynman parameter integral, and have been unable to reproduce the textbook result. I wish to verify the identity $$\frac{1}{ABC} = \int\limits_0^1\int\limits_0^1\int\limits_0^1dxdydz\frac{2\delta(x+y+z-1)}{[Ax + By + Cz]^3} ~\hat{=}~I.$$ We can use the delta function to do ...
I've been asked to find the uncertainty in position for the harmonic oscillator where: $$\langle\hat x^2\rangle = \sum_{k}\langle\Psi_{0}|\hat x|\Psi_{k}\rangle\langle \Psi_{k}|\hat x|\Psi_{0}\rangle $$ With the closure operator inserted in the sum for the harmonic oscillator. I've been given: $$ \hat x = \sqrt{\frac...
If you were trying to scatter a photon, what would be the best thing to try to fire at? Another photon? An electron? A proton? Does the energy of the thing I'm firing increase the probability of scattering the photon?
I want to devise a simple procedure that can be followed by students to discover that a current in a wire produces a magnetic field near that wire. I am of course restricted to very simple materials, but I do have a strong neodymium magnet with which the students magnetize needles, which we then use to discover and map...
In earthen pot water molecules lose heat energy, so where is the temperature drop more - on the pot's surface or inside water?
As the point $A$ is earthed we know that its potential is zero, same is true for point $B$. Due to the cell between $B$ and $C$ we can say that potential at $C$ is $-3V$. So the potential at point D is $-3V$. Due to the cell present between points $D$ and $E$, the potential at E is $-9V$. Now we know that current flow...
If we derive velocity in air when setting air resistance to $kv$, we'll get $$v= \frac{mg}{k}\left(1-e^{\frac{kt}{m}}\right) $$ and if air density goes to $0$, $k$ will also goes to $0$. When $t=T$ (certain number), $ \lim_{k\to 0}v=gT $. This matches my expectation. However, if we graph $v(k, t=T)$ with respect to $...
My answer would be the longer the focal length, higher the magnification will be, resulting in a larger image. But in a ray diagram, how does it look? I am searching for a comparison of ray diagram between short focal length and long focal length but didn't manage to get anything. My high school textbook didn't explain...
I've heard it so many times: "At 0 K Fermi energy and Fermi level are the same." "The Fermi level for an intrinsic semiconductor lies at the middle of the band gap." And the definition of the Fermi energy is The highest level of energy up to which electrons are filled. Now my confusion is if Fermi energy is an e...
I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Quantum Mechanical Harmonic Oscillator, the author says the following: Fig. 2.6 shows the vibrational levels in a PE [potential energy] diagram for the quantum mechanical harmonic oscillator. In th...
I'm currently building a crossbow and was wondering how I might improve the performance of it? I was suggested to fine-tune the rubber band more and maybe change the projectile maybe to a zinc alloy one instead of the plastic ones I use. I do understand this is sort of engineering feat but I think it wouldn't hurt to...
What i read about binding energy is that it is the energy released when nucleus is formed due to the attraction of the strong nuclear force between nucleons. But even after the nucleus is formed, the nucleons are attracted, so why don't they release their energy continuously and lose their mass completely or why does t...
We can turn or zigzag while driving a car, and its yaw rate value changes consequently. From what value of the yaw rate (deg/s) can we consider that the driver has made a dangerous maneuver?
I came up with what might be considered a strange conclusion when thinking about time dilation, and more specifically the Hafele and Keating experiment from 1971. It was shown that time either went faster or slower depending on which direction the plane was traveling in. Since time was measured using an atomic clock wh...
Why we extend $\theta$ from $(0,2\pi)$ to $(-\infty, \infty)$? I mean we cannot measure $\theta$ in experiment, can we? Secondly,the feature of vortex solution (at least in KT transition) can be summarized as the following: have singularity and multi-valued. I'm wondering is this the definition of vortex in mathematic...
Can someone please clarify why the horizontal pressure on the wall is 0.5 x $\gamma$ x $h^2$? Is this because F = P x dA, and P pressure is $\rho$ x g x h. Integrating P x dA gives you 1/2 x $\gamma$ x $h^2$
Details given in the question. Initial Position vector was $(x_₀,y_₀)$ Initial Velocity vector $(v_ᵪ,v_ᵧ)$ Magnitude of acceleration - $a$(constant) $x$ is position in horizontal direction $y$ is position in vertical direction Acceleration vector -$a \frac{x\hat{i}+y\hat{j}}{\sqrt{x^²+y^²}}$ How to find position vector...
It seems that all the literature (just to name a few: Phys. Rev. Lett. 124, 166804, Phys. Rev. Research 2, 013330, Phys. Rev. Lett. 123, 073601, and Phys. Rev. Lett. 123, 256402) says yes to the question in the title, but I find for the moment only one paper mentioning "nonzero energy corner states". Anyone can provide...
I've been looking into how hydraulic lifts work and i don't quite understand yet how Pressure and Forces relate. Let's assume the water is on equal level on both sides and i apply a force to The smaller Area A is amplified by a factor B/A on the other side at Area B, But when do these forces equal out? Because assuming...
For verifying the gauss law in sphere we have same theta between E and A, have symmetrical and uniform electric field. But when we talk about a cube than we get symmetrical electrical field but we do not get same the between E and A at every point.we also doesn't get uniform electrial field as in sphere. so how can w...
Does a charged particle traveling along the y-axis with a constant velocity $v_0$, who enters a uniform electric field pointing at the x direction (i.e perpendicular to the electric field) gain kinetic energy by the time it leaves the electric field?
Which condition(s) should the energy satisfy, such that the solution of the corresponding Euler-Lagrange equation is oscillating?
If the total charge is $0$, why should the dominant term be the dipole? Also, for a dipole consisting of only two opposite charges separated by a distance $d$, i dont understand how can there be higher multipole contributions(since there are only two charges)?
If you gain electric potential energy, is the magnitude of the EPE equal to the work done by the particle in the electric field? Or is the magnitude of the EPE equal to the work done on the particle?
What is the difference between lattice and superlattice ? Can anyone describe with a schematic figure? I have encountered superlattice in the context of bose hubbard model. Also what are the advantages or disadvantages in superlattice compared to lattices in this context?
From Paul Ginsparg's lecture note on Applied Conformal Field Theory, I am given the followings. In $\mathbb{R}^d$, the infinitesimal transformation is given by $x \rightarrow x+\epsilon$ which leaves the metric to transform as $$g_{\mu\nu} \rightarrow g_{\mu\nu} +\partial_\mu \epsilon_\nu+\partial_\nu \epsilon_\mu + O(...
I was wondering the most suitable Gaussian Surface to choose that would allow me solve the electric field easily. Given 2 insulating infinitely long plates that have charge separation. We need to find the Electric Field Intensity at points 1,2 and 3 respectively. What would be the most suitable Gaussian Surface to cho...
... c/2-(-c/2)=c relative to the other object? (title character limit) Alternatively If my speed is c/n to the object behind me, which also has c/n to the one behind it and so on I should have a speed of c to the observation of the nth or so object behind. If n is a large number none of the objects are moving unreason...
From Sakurai, unitary equivalent observables have identical spectra. $$ A |a\rangle = a |a\rangle, $$ $$ UAU^{-1}U|a\rangle = aU|a\rangle $$ Which can be written as, $$ B|b\rangle = a |b\rangle $$ where, $$ B = UAU^{-1}$$ However, if I'm not wrong, this works when the unitary transformation U is time-independent. What...
I have a problem understanding how changing the boundaries from a periodic lattice to a finite lattice. For example, if we have a 2D square lattice of lattice constant $a$ whose $x$ axis has only $N_x$ cells with one atom each and no spin degeneracy, and periodic boundary conditions on $y$ with $N_y$ cells, how can we ...
Is it possible somehow to achieve gravitational shielding? Are there any experiments presently going on or future projects?
Recently I came across a question which stated- A calorimeter of water equivalent 40 g contains 80 g of ice at 253K. What does this statement mean? Does it mean that the calorimeter contains 40 g water and 80 g ice at a temperature 253 K? If the calorimeter contains ice at 253 K , is the temperature of the calorimeter ...
If I apply Coulomb's Law, I get that the field is defined in all space for volumetric densities. For linear and surface charges, the field is undefined where the charges are (division by $0$). Why wouldn't $ \mathbf{E}=\vec{0} $ inside an infinite line, or plane, as intuition suggest? Why wouldn't $ \mathbf{E} = \vec{...
I have recently come across this topic of equipotential surfaces. I have a very basic doubt: Q.) Let's say we are talking about a point P inside the equipotential surface(eg:sphere). Now, before considering the equipotential surface let's beforehand calculate the potential at point P. After calculating, condsider the e...
I have learnt in the lecture that the symmetry factor of the following diagram is 1/2: where the line corresponds to a gluon. But why is this the case? We get 1/2 from 2nd order in pertubation theory. Then we get a factor of 2 for the interchangeability of the internal vertices, a factor of 3*3 for the connection of ...
Today we started learning about Biot-Savart law. While deriving the formula, our professor listed out a bunch of relations, which have been experimentally determined, ->dB is directly proportional to current, length of element, and inversely proportional to square of distance. This all seemed ok and relatable, and th...
The 3 Newton's laws of motion are easy to be understood but examples citing which law caused it are so confusing - say a bullet fired from a gun - many people state it cause is 3rd Law - but I see all 3 laws are applied: First law causes the bullet change its state of inertia - second cause the bullet gained momentum a...
Is there an actual definition of characteristic time? When dealing with heat transfer for instance convective heat transfer between a naked flame and a fluid in a glass bulb, can characteristic time be defined as: the time taken to for the centre of the fluids temperature to be a certain percentage of its surface tempe...
I was reading this in my textbook and I don’t understand how absorbing radio waves creates an alternating current in the conductor. Please refrain to simple explanations, I am just a tenth grader.
How can I tell how many solutions I will have for an electronic Schrödinger equation ? For example, solving it for the hydrogen atom we get infinitely many solutions \begin{equation} H_e(\mathbf{R})\Psi_i(\mathbf{R},\mathbf{r}) = E_i(\mathbf{R}) \Psi_i(\mathbf{R},\mathbf{r}), \qquad i = 1, 2, ..., \inft...
I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Infrared Absorption Process, the author says the following: The typical IR spectrometer broadband source emits all IR frequencies of interest simultaneously where the near-IR region is 14,000 - 400...
My question is how to define a Goldstone Mode? Initially I thought that Goldstone Mode is a consequence of spontaneous symmetry breaking, but later I learned that in Kosterlitz–Thouless transition, the spontaneous symmetry breaking is absent but we still have Goldstone Mode there. To make it more self contained,the r...
Why does the rate at which a capacitor in an RC circuit charges, only depend on $R$ and $C$? We know that for power $$P = \frac{V_{\text{emf}}^2}{R} e^{-t/RC}=\frac{QI}{C} $$ so why are we ignoring the effect of changing $V_\text{emf}$ on the current and power?
Are there alternatives to Calabi-Yau spaces describing dimensions in superstring theory? If yes, what are they? If no, why?
We use time independent schrodinger equation to find Stationary state solution for some potentials. My question is that, these Stationary state solutions are physically reliable or not? I am asking this because these solutions provide us state of definite energy i.e, we can measure energy with zero uncertainty. But phy...
A free, massless scalar theory, $\mathcal{L}_1=\frac{1}{2}(\partial\phi)^2$, is scale-invariant both classically and quantum mechanically. However, a $g\phi^4$ theory, $\mathcal{L}_2=\frac{1}{2}(\partial\phi)^2-\frac{g}{4}\phi^4$, is not because even though the Lagrangian is scale-invariant the Greens functions are not...