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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Successor to Copenhagen Interpretation as Orthodox Interpreation of Quantum Mechanics

First, I read the questions FAQ for this and I hope this does not violate the rules. I am not asking for personal opinion, but for observations of hard evidence of trends on this subject. When I ...
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1answer
31 views

Expectation value position of sine wave in infinite square well

Given a neutron (mass$\approx$939 MeV/c$^2$) in an infinite square well of size $a$, the value of the expectation value for position should be in the range $[0-a]$. I know that the general form of the ...
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1answer
81 views

Crystal field in diamond

The crystal field effect occurs in ionic crystals and causes a splitting of the magnetic quantum levels of the cation. The magnitude of the splitting may be roughly computed by obtaining the potential ...
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4answers
509 views

How do you find a particular representation for Grassmann numbers?

This question is more general in the sense that I want to know how one finds a particular (say matrix) representation for any object. For the case of Grassmann numbers we have from Wikipedia the ...
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1answer
59 views

Can a particle have an imaginary mass?

Now, I'm not very involved in the physical sciences, beyond some high-school classes - though I did listen to some college lectures for physics. I was reading "Do Tachyons Exist?" by John Baez, which ...
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1answer
23 views

Degenerate perturbation theory

I don't understand the part about turning off the perturbation. What is meant by or what is he referring to when he says "upper" and "lower" states. Why must the "upper" state reduce to a ...
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1answer
59 views

Which non-Copenhagen interpretations of Quantum Mechanics have actually produced something useful?

The question has most of it in the name. "Useful" may be interpreted as: measurably different from Copenhagen interpretation and true potentially measurably different and potentially true (i.e. not ...
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1answer
174 views

Thought Experiment: Force on magnets in a Stern Gerlach Experiment

Background: In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets. "Measurement" takes place when a screen is placed on one end, blocking one ...
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1answer
67 views

Why is particle superposition still part of quantum mechanics? [duplicate]

After reading an article on Schrodinger's Cat, it seems that if we take the environment as an observer, that superposition cannot occur because all atomic and subatomic entities would be observed all ...
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0answers
46 views

Does an expectation value over only part of a wavefunction have physical meaning?

Does the expression: $$\langle p\rangle_{x=a, b} =\frac{\int_a^b \Psi(x)^*\,\hat{p}\,\Psi(x)dx}{\int_a^b |\Psi(x)|^2dx} $$ have any physical meaning when $\int_a^b ...
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2answers
323 views

A quantum particle which is almost at rest but whose position is random!

Assume a particle is given by a quantum state which is constructed in such a way that it is equally probable to find it anywhere in an fixed interval $(0,L)$ but has arbitrarily low velocity. The ...
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1answer
220 views

Reason for decoherence time's dependence on variables?

Zurek 2001 is a review article on decoherence in quantum mechanics. Equation 5.36 on p. 24 gives an estimate of the decoherence time, which I'll paraphrase as follows: $ \frac{t_D}{t_R} = ...
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1answer
247 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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1answer
21 views

Fetter & Walecka's derivation of second quantised potential term in many-particle TDSE

For the potential term in the Hamiltonian, I understand that we go through the same process as with the kinetic energy term. On the RHS of the TDSE, we get something like ...
45
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5answers
4k views

Trace of a commutator is zero - but what about the commutator of $x$ and $p$?

Operators can be cyclically interchanged inside a trace: $${\rm Tr} (AB)~=~{\rm Tr} (BA).$$ This means the trace of a commutator of any two operators is zero: $${\rm Tr} ([A,B])~=~0.$$ But what about ...
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0answers
15 views

What is the correct setting for Kirchhoff's Law of Thermal Emission?

For example, is the setting free space? Is it a surface? etc. So, what is the correct setting of Kirchhoff's Law of Thermal Emission?
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18 views

Why does the interference patterns in delayed choice quantum eraser cancel out? Why/how does it have a phase shift?

Talking about this experiment https://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser#The_experiment_of_Kim_et_al._.282000.29 I am assuming that anyone able to answer my question is already ...
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2answers
76 views

Meaning of the general matrix element $\langle x'|O|x\rangle $

In a recent lecture we were told that $\langle x'|\hat{O}|x \rangle = O(x,x') = O(x)\delta(x-x')$ "due to the locality of quantum mechanical observables". I have no idea what this is supposed to ...
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0answers
20 views

Multiple contemporary measures of a photon's state

From quantum mechanics, when you polarize a photon using computational base and you try to measure its state using a diagonal base, you'll get with the 50% of probability $|0\rangle_{{} + {}}$ or ...
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3answers
34 views

How does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?

So we are looking at central potentials in QM; The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$. We have; ...
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1answer
50 views

$[a,a^{\dagger}]=1$ or $[a,a^{\dagger}]=I$

$[a,a^{\dagger}]=1$ or $[a,a^{\dagger}]=I$? On every book i read $[a,a^{\dagger}]=1$. But doesn't $a$ have infinite dimension? So why does the commutator go to a number which is one dimensional?
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3answers
90 views

How bizarre can the Quantum two slit experiment get?

Note 1: Don't apprehend my question as 'quantum woo'. I do not mean so and hate anyone who does. Note 2: I am just a 14 year old physics enthusiast. Don't expect any background. On to the real ...
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5answers
3k views

Complex Conjugate of Wave Function

I've been reading through Griffiths QM book, and the only thing bugging me is they never fully described what $\Psi^* $ should be for any given function. I know it's the complex conjugate at the same ...
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2answers
891 views

Weyl exponential form of the Canonical Commutation Relations

What is the physical meaning of the $c$-numbers $Q, P\in \mathbb{R}$ in the exponent of the Weyl system $\exp\left[\frac{i}{\hbar} Q \hat{p}\right]$ and $\exp\left[\frac{i}{\hbar}P\hat{q}\right]$? ...
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3answers
413 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
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25 views

Momentum Operator [on hold]

Hello Community, I'm writing a paper on quantum mechanics and have a question about following formulas and the derivation of them. It's in german but I was told that I have an error somewhere in the ...
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1answer
127 views

General formulation for fermions

Let us look at a set of fermionic creation and annihilation operators $b_n$, $b_n^\dagger$ with $n \in \mathbb{N}$. What is the precise relationship between this and this sequence here (partition ...
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0answers
26 views

Classical Quantum or Relativistic?

An ensemble contains free electrons at 10^3 electrons per m^3 at 10^7 K. What can this ensemble be treated as: a Classical Quantum or Relativistic gas or in some overlapping domain?
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0answers
46 views

Loss of interference in single-photon Mach–Zehnder interferometer with detector in only one arm

I have read that if you have a Mach–Zehnder interferometer (doing a single-photon experiment) and put a non-destructive detector in only one of the two arms (connected to the first beam splitter), you ...
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1answer
49 views

Conservation of energy in quantum mechanics

In Griffiths' book Introduction to quantum mechanics (second edition, page 37) it states: The time-independent Schrödinger equation says $$\hat{H} \psi_{n} = E_{n}\psi_{n}$$ so $$\langle H ...
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3answers
1k views

Do electrons in an atom always have the same 'direction'?

Perhaps speaking of direction of an electron isn't quite correct. But does QM indicates a kind of way whether all electrons are going e.g. 'clockwise' or not? Of course QM just gives a probability ...
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6answers
11k views

Compton scattering vs. photoelectric effect

Say a photon hits some atom. What determines whether there will be a photoelectric effect (photon is absorbed, electron is released) or whether there will be a Compton scattering (the photon is ...
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0answers
13 views

When you make materials smaller is there a trend in the manner light is absorbed or reflected?

For instance if you take gold is shines like yellow, but if you make it smaller I've heared that it absorbes more the smaller frequencies. At a size of 100nm a piece of gold will absorb fe more blue ...
2
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1answer
31 views

What is the correct statement of Kirchhoff's Law of Thermal Emission?

There are various quite different statements in textbooks and other science literature as to Kirchhoff's Law of Thermal Emission. So, what is the correct statement of Kirchhoff's Law of Thermal ...
3
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1answer
485 views

Hubbard Model Hamitonian

$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$ is defined to be a Hamiltonian for modeling quantum random walk of identical ...
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0answers
20 views

density of states with changing potential floor

I wish to calculate the density of states for a 1D finite potential well, for the scattering states, meaning $E>0$. I have a potential of the form: $$ V(x)=\begin{cases} -V_0 & |x|<a\\ 0 ...
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7answers
1k views

How can a product of Bra and Ket be a scalar if they are matrices?

I am trying to teach myself Quantum Mechanics and am currently on Complex Vector Space Arithmetic. According to Wikipedia, product of a Bra and Ket is a scalar (which, I think, means a complex ...
4
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1answer
104 views

Help needed to understand “On the reality of the quantum state”

I am having trouble to understand the reasoning in the following paper, On the reality of the quantum state. MF Pusey, J Barret and T Rudolph. Nature Phys. 8, 475–478 (2012); arXiv:1111.3328. ...
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1answer
167 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 ...
2
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5answers
89 views

Is QM something that belongs to all relative small particles or only to subatomic particles? [on hold]

For us human beings subatomic particles like elektrons are described by the laws of QM. But imagine their is a very huge giant looking on the universe. For him all the planets and stars are so tiny ...
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1answer
57 views

Physical meaning of weight function in inner product in Quantum Mechanics

When taking the inner product of say two functions in Quantum Mechanics,we include a weight function w(x,y,z) that is usually equal to unity(in my undergraduate introductory QM course anyway). But ...
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0answers
37 views

Are there some explication for the wave function in Quantum Mechanics? [on hold]

I start to learn the Quantum Mechanics and I don't really understand the mechanisme behind the wave function. As what I feel and as I think the world as multivers, 1/ I see wave function like a way ...
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0answers
40 views

Spinor on an eigenstate of $J_z$ [on hold]

The state of a particle with spin 1/2 is described (in the $S_z$ representation) by a spinor $[\Psi]=\left( \begin{array}{c} \phi_+ \\ \phi_- \\ \end{array} \right)$ Its known to be eigenstate of ...
2
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1answer
511 views

Classical limit of the path integral formulation of quantum mechanics

It is well-known that if $S \gg \hbar$, then the classical path dominates the Feynman path integral. But is there some to show that if $S\gg\hbar$, then the particle's trajectory will approach the ...
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1answer
47 views

What is the origin of the quantum operators for p and E? [on hold]

It is always stated the quantum operators for p en E are the ones we´re familiair with. But where do these operators come from?
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1answer
200 views

Single quantum particle in beam splitter, with different systems located in each channel

Suppose a quantum mechanical particle enters a beam-splitter, which sends its wave packets into two mutually orthogonal channels, $C_a$ and $C_b$. Suppose that $C_a$ also contains System A, with ...
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2answers
177 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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0answers
53 views

What would be the research advances if we discover the gravitational waves? [on hold]

As researchers of LIGO (USA) and VIRGO (France/Italy) say that they have discovered gravitational waves thanks to black hole collision today, what would be, apart of the important confirmation of ...
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0answers
25 views

Restriction to the total angular momentum of two identical particles with spin 1

I've been asked if there is any aditional restriction to obtain the possible values of the total angular momentum J by considering that the 2 particles of spin S=1 are identical. If they are not ...
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0answers
34 views

Proving Probability Current and Momentum relationship

I am trying to show that $\mathbf j = \frac{\hbar}{2mi}\left(\Psi^* \mathbf \nabla \Psi - \Psi \mathbf \nabla \Psi^{*} \right) \,, $ simplifies to $\mathbf j = \frac{\mathbf p}{2m} (|\Psi|^2) $. I ...