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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22 views

Pion decay into electron and anti-neutrino

In Peskin and Schroeder Books Chapter 5 subsubection Bound State equation (5.43) $\mathcal{M}(\uparrow \uparrow \rightarrow B)=\sqrt{2M}\int ...
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0answers
25 views

Hamiltonian for semiconductor

I was wondering which terms we need in a semiconductor Hamiltonian where no transition between the valence and conduction band occur? First we would have a term describing the energy of the full ...
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1answer
26 views

Centrifugal Term

I'm studying quantum mechanics with Griffiths (2 nd edition) and I have one question related to the Schrodinger equation in spherical coordinates. In the radial equation: ...
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2answers
78 views

How do we know $\psi$ depends on $n,l,m$

Regarding the separation of $\psi$ to an angular and radial part, why does each part have a specific dependence of the quantum numbers? How can Schrodinger equation describe a system just from its ...
2
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1answer
157 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
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0answers
26 views

Quantum Localization

Hi every body, Could someone please give me clarification and explanation about localization, localization length and Quantum localization? All i know is that it has something to do with diffusion. ...
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2answers
92 views

An attempt to understand Quantum mechanics [on hold]

Can I learn quantum mechanics just by knowing basic calculus and algebra? I know basic differential calculus and integral calculus. I am willing to study to understand what quantum mechanics means. ...
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0answers
43 views

Diagrammatic Calculus and quantum mechanics

I came across this paper http://arxiv.org/abs/quant-ph/0510032 I don't understand it very well, but they basically show that they can reduce quantum mechanical calculations to manipulation of some ...
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1answer
29 views

Why does a quantum cloner imply superluminal communication

I am wondering why superluminal communication would be possible if a quantum cloner would exist? The common argument (FLASH) goes as follows: Alice and Bob share the Bell state $$ |\psi^-\rangle = ...
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0answers
33 views

Corrections to the Equipartitio theorem

Does anyone know why sometimes $E = \frac{3}{2}k_{b}T $ is written as $E = \pi k_{b}T$. Where does this come from?
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1answer
18 views

How to prepare the Stern-Gerlach experiment for a particular state

If we want to form a diagram or calculate the angles at which the magnets need to be positioned in the Stern-Gerlach setup,how do we proceed? For example, if I want to prepare the following state, ...
0
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1answer
90 views

Spin operator eigenstate in Fock space

I am creating an operator group from representation of spin 1 operators $$J_{x} = \frac{1}{\sqrt{2}}\left(\begin{array}{ccc} 0 & 1 & 0\\ 1 & 0 & 1\\ 0 & 1 & 0 \end{array} ...
2
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1answer
76 views

Why is the full eigenfunction a product of eigenfunctions and not a sum?

For example suppose there is a two electron system. Why is the full eigenfunction a product of the spatial eigenfunction and spin-wave-function for the two electron system?
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2answers
47 views

Probability from classical physics compared with quantum mechanics

$|\psi\rangle$=$\frac{1}{\sqrt5}|\uparrow_z\rangle+\frac{2}{\sqrt5}|\downarrow_z\rangle$ a)What is the probability of obtaining $+\frac{\hbar}{2}$ for $S_x$? b)If after obtaining ...
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0answers
18 views

Probability from classical physics compared with quantum mechanics [duplicate]

$$|\psi\rangle=\frac{1}{\sqrt5}|\uparrow_z\rangle+\frac{2}{\sqrt5}|\downarrow_z\rangle$$ a)What is the probability of obtaining $+\frac{\hbar}{2}$ for $S_x$? b)If after obtaining ...
5
votes
5answers
287 views

Can we change a photon's frequency in mid-air?

Can we have a light source emitting photons in the infrared range and after, lets say, 5 meters, these photons become a photon in the x-ray range? The only way I know we can change a photon's ...
7
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3answers
320 views

Quantum Entanglement Versus Inflation in the Early Universe?

Quantum entanglement is one of the most fascinating and mysterious phenomena in nature. It needs no interactions, or any sort of exchange for it to take place. It is possible, not against any rules of ...
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2k views

Is it possible to see atoms ? There's a wikipedia picture

As per my knowledge atoms are smaller beyond our imaginations But there is a wikipedia image which shows silicon atoms observed at the surface of silicon carbide crystals. Here's the link to the ...
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2answers
686 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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0answers
15 views

With quantum entanglement, why does the spin of a particle depend upon probability when measured is at an angle?

In this video https://www.youtube.com/watch?v=ZuvK-od647c it talks about how the particle's being spin up or down when measured at an angle depends on this probability: cos^2(theta/2). Why is it ...
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2answers
564 views

How are anyons possible?

If $|ψ\rangle$ is the state of a system of two indistinguishable particles, then we have an exchange operator $P$ which switches the states of the two particles. Since the two particles are ...
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0answers
46 views

How to find creation and annihilation operators? [duplicate]

I get confused when trying to find this. Please describe it as simply as possible, but keep in mind I have no budget whatsoever to pay for textbooks, so here goes: How do you find the creation and ...
3
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0answers
94 views

Why is imaginary time “outdated”? [on hold]

I was looking at reviews for Sakurai's Quantum Mechanics textbook, and some mentioned it being outdated, specifically mentioning his use of imaginary time. Is this idea deliberately avoided in modern ...
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1answer
82 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
6
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1answer
353 views

Have they really photographed light behaving both as a particle and a wave?

I just came across this article where they are claiming that they have photographed light behaving both as a wave and a particle! The paper has been published in Nature Communications and I read the ...
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0answers
34 views

Spectral lines and QM

In the various presentations I've seen so far in atomic physics of series such as the Balmer series, the wavelength of each spectral line is definite - but in QM, free particles have no definite ...
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1answer
52 views

Are there nonlinear models of quantum mechanics which forbid superluminal signaling?

What would a nonlinear model of quantum mechanics which forbids superluminal signaling look like? Of course, a nonlinear $\psi$-ontic theory with entangled states could have superluminal effects upon ...
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19 views

Lindhard function for surface plasmon

Is there anybody that knows how to calculate the Lindhard function for the surface plasmon (between the surface of two metals of different dielectrics)? What I'm looking for is to find this function ...
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2answers
34 views

Allowed system energies from quantized Hamiltonian spectra

To find the allowed energies for a system, I can find the spectrum of the Hamiltonian $\hat{H}_{\psi}$ given a wavefunction $\psi$ representing the state of the system. 3 cases might happen: either ...
0
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1answer
15 views

Particle on a ring model for electron motion in Porphine and highest occupied state

I'm studying for a test and I came across the following question: The particle on a ring is a useful model for the motion of electrons around the porphine ring. We may treat the group as a ...
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2answers
124 views

Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
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2answers
387 views

Compton scattering multiple wavelengths?

The formula given for compton scattering shows that when x-ray of one specific wavelength hits carbon or some materials, emitted x-ray will be of one new specific wavelength. However, according to ...
1
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1answer
26 views

How are energy states of photons reason for frequency independence in Compton scattering

I am reading on Compton scattering, more specifically on how Compton interpreted his results. He observed that the frequency of the scattered radiation was independent of the material used, so he ...
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2answers
85 views

Flow of electrons in electric current

In an electric circuit, how does the excitation of the free electrons to higher energy levels translate into net forward motion of the electrons to the positive terminal? My concept of electrons ...
0
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1answer
53 views

Interpretation of Fermi-Dirac statistics

I was reading that as temperature increases the energy at which $n(E)=0.5$ shifts to lower energies as these lower energy states become depopulated. Could someone explain that, what it means and why ...
2
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1answer
107 views

Integral over a product of two Green's functions

Need some help here on a frequently encountered integral in Green's function formalism. Forgive me since I am a junior student. I have an integral/summation as a product of a retarded and advanced ...
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0answers
27 views

Partial diagonalization of the Fock matrix

I'm currently writing my dissertation on the application of SCF semi-empirical methods to large systems, in particular proteins, and I'm stuck with a problem: I don't understand why, given the fact ...
3
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0answers
134 views

What concepts could I teach to children in a game about quantum-mechanics? [on hold]

I think that games can also be used to teach things to young people or childs, different than for example a book and could be more "direct" than teaching them all the math background, I would like to ...
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3answers
49 views

Energy of system in eigenstate of Hamiltonian

I know how to find the spectrum of the Hamiltonian to get the allowed energies for a system. If the spectrum is quantized, I can get definite values for each energy level. But when the system is in ...
3
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2answers
232 views

Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
0
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1answer
33 views

How much time between measurements do you have in order to make the same measurement on a particle?

As I understand it, you can make a measurement on a particle and if you quickly carry out a second measurement you will get the same outcome as the prior measurement. If this is the case, how much ...
0
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1answer
43 views

Neutrino mass and the Majorana equation

I can't seem find this on the Internet. What does the Majorana equation predict neutrino masses to be (if they were their own antiparticle), and how? (I have little understanding of spinors, btw...) ...
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0answers
33 views

WKB Quantization Condition - negative?

In deriving the quantization condition for a bound state in a potential with "no verticle walls" we start with the WKB connection formulas to find the wavefunction in the interior of the well ...
2
votes
1answer
120 views

Floquet quasienergy spectrum, continuous or discrete?

I haven't got a feeling about Floquet quasienergy, although it is talked by many people these days. Floquet theorem: Consider a Hamiltonian which is time periodic $H(t)=H(t+\tau)$. The Floquet ...
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2answers
226 views

Measurement of the energy of an atom using a cold substance

An atom was prepared in a superposition of ground state and excited states.I propose to measure the state by coupling the system to a cold enough substance. By cold enough I mean $$kT\ll E_1,$$ where ...
4
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3answers
259 views

What exactly is a bound state and why does it have negative energy?

Our professor hasn't explained what bound states are. Could you give me an idea of what they mean and their importance in quantum-mechanics problems with potential (e.g. a potential described by a ...
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0answers
14 views

What are the conditions of wave function continuity when solving for Dirac Spinors as done in “Klein paradox” paper by Novoselov?

In the paper "Chiral tunneling and Klein paradox" paper by Katsnelson, Novoselov, and Geim, they use the wave function for Dirac spinors. What are the conditions for continuity of the wave function ...
3
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0answers
74 views

How to check whether Schrödinger's cat was in superposition of states?

Suppose we can make an arbitrarily precise preparation of a Schrödinger's cat (and isolate it arbitrarily well so that decoherence is not a problem). If we prepare lots of cats in this state, what ...
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1answer
30 views

Why does negative energy imply that a system is bounded? [duplicate]

I wanted to know why "negative energy" of a two particle system implies that it is bounded. That is what happens in the case of a hydrogen atom; my textbooks say so, but they do not give any reason ...
6
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2answers
83 views

Triangular barrier in infinite potential well

Suppose I am looking to solve the wavefunction for the following 1D potential: $$U(x) = \begin{cases}V_0\frac{a-|x|}{a}&\quad\text{for}\quad|x|<a ...