Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the ...

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Question about the exclusion principle

I understand the Pauli exclusion principle like this: For two electrons to occupy the same state their spins must be opposite. If the two electrons are in different states (different spatial ...
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1answer
89 views

Kronig-Penney model

I am studying the Kronig-Penney model as treated in the book by Kittel: Introduction to Solid State Physics. In this model one considers a period potential which is zero in the region $[0,a]$ ...
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135 views

Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle ...
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71 views

Energy of an Electron in a One Dimensional Periodic Potential

First, we consider the time independent Schrodinger equation of the form: $$\bigg(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+u(x) \bigg)\phi_A(x)=E_A\phi_A(x)$$ Where $u(x)$ is a potential created by a ...
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Why should multiplication of a ket vector by a complex number change only its “direction”?

Dirac argues on page 17 of his book, The Principles of Quantum Mechanics, that multiplication of a ket by a complex number shouldn't change the state this ket represents. But then concludes: Thus ...
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37 views

Forward-scattering off a potential well

In his book, James Binney writes the following: My question is what is the meaning of this expansion as $1+T$? I say this because you don't tend to consider the possible "paths" that a particle ...
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93 views

Any ket as a sum of eigenkets of a given observable

Most quantum mechanics texts include a phrase such as 'any ket can be written as a sum of eigenkets of a given observable'. I have problems with the generalities of any ket. Does this literally mean ...
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2answers
58 views

Using bra-ket notation?

Am I using Bra-ket notation correctly? I want to define a superposition of the states, $|0\rangle$ and $|1\rangle$. Is it simply? $|0\rangle + |1\rangle$ I can't find any non-technical information ...
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36 views

What is the mechanism for equilibration?

I read on page 5 of Matthew Schwartz' book QFT & the SM that if you heat a box with monochromatic light, then (later) all the frequencies will get excited. The author says that particles have to ...
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28 views

Capacitor with big space of insulation and polymer inside

The capacitor has insulator and it is covered by two conductors from top and bottom. I started to think if this insulation part can be wide like 1 cm big - yes, it can but then permittivity has to be ...
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154 views

Electrons skip randomly around their orbits

I read where the electron (as well as a few other particles) skips around in its orbit randomly rather than move around the orbit smoothly. This effect has been repeatedly observed in the laboratory ...
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101 views

Why is the orbital angular momentum of a pi electron along the axis of two atoms' molecule one?

I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary ...
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54 views

Hugh Everett's MWI [closed]

According to Hugh Everett's many worlds interpretation, all the possibilities of one action can happen at the same time in other parallel universes, so how come we can't see these worlds? now I bumped ...
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1answer
83 views

Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
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2answers
50 views

Quantum Eraser thought experiment with light photons of distinct color

I tried to recreate the Quantum Eraser experiment into a thought experiment with a few changes. It left me a little perplexed as to what outcomes I should expect. Any help would be appreciated. Lets ...
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1answer
446 views

How to solve bound states of 2D finite rectangular square well?

I want to solve bound states (in fact only base state is needed) of time-independent Schrodinger equation with a 2D finite rectangular square well \begin{equation}V(x,y)=\cases{0,&$ |x|\le a ...
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1answer
31 views

Is something beyond the material needed to solve the Von Neumann Chain?

A problem has been presented that goes like this: Particles normally exist as several mathematical possibilities rather than one actual object. It is said that in the absence of observation, ...
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33 views

Energy from the Feynman-Kikuchi Partition Function

The Feynman-Kikuchi Partition function is given as $$Z_{FK}=K_\beta \int dx \eta(x) \exp \left(-\frac{x}{\beta}\right) $$ where $K_\beta$ is a normalization constant and ...
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1answer
78 views

Doubt in a certain equation of a research paper [closed]

In the following research paper (link provided) , I am not able to figure out how do we get the equation (7) . Please help me out. Also , please recommend the necessary pre requisite text to ...
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1answer
27 views

Expected value $<\hat{x}>$ of: $\Phi(x,t)=Ne^{-a[(Mx^2/\hbar)+it]}$ is infinite, why?

The problem says: A particle of mass $M$ is described by the wave function: $$\Phi(x,t)=Ne^{-a[(Mx^2/\hbar)+it]}$$ where a is a positive constant. Asked to determine such things as the ...
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24 views

Spontaneous emission in a system with multiple sublevels

I have been trying to compose proper rate equations for density matrix of a 2 level system with multiple magnetic sublevels, and I have run into difficulty with including spontaneous emission terms in ...
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75 views

Classical probability explanation for quantum non-locality and Bell's inequality? [closed]

The question is whether this solution is true or false, and if there is an error, please point what is it and where is it. Classical probability with local causality solution, just like tossing two ...
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430 views

How do photon emitters and photon detectors work?

The interpretation of the double slit experiment is very strange and i want to understand how they did it before I give up my concept of reality. With the double slit experiment a interference pattern ...
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2answers
75 views

2-slit experiment

In the 2-slit experiment, is it possible to "account" for all of the energy in the incoming beam - i.e. does all of the incoming energy show up in the bright spots or is some of it "destroyed" when ...
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67 views

Quantum Excitations

In the context of quantum field theory, is the schrodinger or dirac equation actually describing some sort of an actual wave in some field like light in EM field ? So all particles are actually waves ...
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21 views

Splitting of degenerate energy levels with a perturbed particle in a box

Suppose you have a particle in a square box $[0,L]\times[0,L]$. As the box is a square, the (2,1) and (1,2) eigenfunctions will have the same energy. If you were to apply an oscillating electric field ...
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1answer
103 views

Is there a formalism for talking about diagonality/commutativity of operators with respect to an overcomplete basis?

Consider a density matrix of a free particle in non-relativistic quantum mechanics. Nice, quasi-classical particles will be well-approximated by a wavepacket or a mixture of wavepackets. The ...
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1answer
312 views

Why doesn't De Broglie's wave equation work for photons?

Well, as I am learning about quantum physics, one of the first topics I came across was De Broglie's wave equation. $$\frac{h}{mc} = \lambda$$ As is obvious, it relates the wavelength to the mass of ...
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1answer
38 views

Eigenfunctions corresponding to degenerate spectra

It is well knwon that an eigenstate can be obtained by superposing wavepackets. In other words, if $\Psi({\bf x},t)$ is the solution of the time dependent Schroedinger equation for an initial ...
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1answer
273 views

Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with knightian freedom the same things in essence?

In his remarkable works (1,2 and their recent development 3) Thomas Breuer proves by diagonalization the phenomenon that the observer cannot distinguish all phase space states of a system where he is ...
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5answers
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Can the photoelectric effect be explained without photons?

Lamb 1969 states, A misconception which most physicists acquire in their formative years is that the photoelectric effect requires the quantization of the electromagnetic field for its ...
6
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3answers
168 views

Entropy and the uncertainty principle

According to the second law of thermodynamics, the total entropy of the Universe must always increase after any interaction (as I understand). So in the hydrogen atom, the electron has a high ...
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220 views

Is quantum tunneling related to imaginary time?

I was studying for my exam and looking at the chapter which talks about Potential-energy graphs. Let's take this as an example: My book states that: "If the object is in $B$ and has a total energy ...
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54 views

Use of Boltzmann over Maxwell distribution

Why is the Boltzmann distribution used over the Maxwell distribution in many cases such as the derivation of Plancks law of thermal radiation, derivation of Einstein A and B coefficients, Langevin ...
3
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3answers
668 views

Can we have discontinuous wavefunctions in the Infinite Square well?

The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
2
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3answers
190 views

How can the reduction postulate be removed with the other postulates of QM still leading to correct predictions?

In the axiomatic presentation of QM, I've seen it stated many times that the reduction postulate is not needed and/or incorrect, and could be gotten rid of. However, without the reduction postulate, ...
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1answer
58 views

Wavefunctions and Quark Confinement

While I have a decent knowledge of general relativity (and, of course, classical mechanics), I am quite a novice when it comes to quantum mechanics, so I apologize if this is a rather basic question. ...
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3answers
443 views

Speed of light, breaking the barrier

when the sound barrier is broken, a series of concentric waves of sound is produced.Does it mean when the speed of light barrier is broken, a ripple of photons are created in the space-time fabric?
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1answer
159 views

Is kinetic energy in QM a state-property or is it distributed?

Suppose we have a quantum mechanical system, which is well described by its wave function in r-representation $\Psi$. We are interested in the properties of an observable, say the kinetic energy $T$. ...
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1answer
89 views

Thermionic emission, delayed emission and predissociation

In molecular photodissociation, the thermionic emission, delayed emission and predissociation are the same? Otherwise, what is the difference between them? My question is not about the solids, but I ...
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1answer
199 views

Density matrix and irreducible tensor operators

I'm reading those lecture notes on atomic physics. Yesterday I posed a question on reducible tensors, and today I have a question on their relation to the density matrix. If there's any information ...
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1answer
252 views

Maximum probability of success for distinguishing between two pure states with one measurement

Suppose you have the states such that $\langle \psi_1| \psi_2 \rangle = \cos(\alpha)$ and you have one measurement to distinguish between the two. It is claimed that the probability of success at ...
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1answer
34 views

Prove the solution of von Neumann equation will never stabilize if Hamiltonian and initial density matrix commutes

Given von Neumann equation $$\frac{d}{dt} \rho(t) = -i [H, \rho(t)] = -i e^{-iHt}[H, \rho(0)]e^{iHt}.$$ If we know that $[H, \rho(0)] \neq 0$, how do we prove in details the solution of von Neumann ...
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54 views

Can we apply Quantum Superposition

Erwin Schrödinger’s famous thought experiment's video presented by Perimeter Institute for Theoretical Physics. From this video can we conclude that , in a macroscopic label we can not have a ...
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6answers
3k views

Disproof of Bell’s Theorem

The half-page arxiv doc by Joy Christian of Oxford Uni, UK has the Title and Abstract: Disproof of Bell’s Theorem We illustrate an explicit counterexample to Bell’s theorem by constructing a ...
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1answer
116 views

Initial condition for Fourier transformed Schrödinger equation

I asked in this thread Time-dependet Schrödinger equation how to solve the Time-dependent Schrödinger equation. One of JamalS' recommendations was the Fourier transform, which is why I want to quote ...
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85 views

Determining the Wave Function From Initial Conditions

This is Problem 2.6 (b) in Griffiths, Intro to QM: A particle in an infinite square well has its initial wave function an even mixture of the first two stationary states: $\Psi(x,0) = ...
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1answer
164 views

Time-orded operator in Srednicki

On page 51 Srednicki states, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order ...
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Is there is a specific original source where the “quantum operator ordering issue” is stated?

During my research, when the quantum operator ordering ambiguity is mentioned is deemed usually in the likes of "the well-known problem of ordering in quantum mechanics". However, could anybody point ...
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1answer
54 views

Young Tableaux for $SU(3)$ representations vs. $j=1$ objects

I'm working through Sakurai's Modern Quantum Mechanics and in the section on Permutation Symmetry and Young Tableaux, he mentions that a tableau constructed of $\square = ...