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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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 don't understand why there is a difference between D1 and D2. On ...
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2answers
71 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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14 views

Expectation value position of sine wave in infinite square well

I know that the general form of the expectation value for position is $$\langle X\rangle=\int_{-\infty}^{\infty}\psi^*x\psi dx \, ,$$ but my wavefunction is $\sin(n\pi x / a)$ where $a$ is the size of ...
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14 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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9 views

Given Quantum operator matrix [M] solve for matrix [A] such that [M] = e(A) where A is the exponent of e

I have a qunatum mechanical initial wave function of the following form: $$(1/\sqrt2)(|D_0\rangle|C_1\rangle + |D_0\rangle|C_0\rangle)$$ where $$\langle D_0|D_1\rangle = \langle C_0|C_1\rangle = 0$$ ...
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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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47 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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1answer
44 views

Why is particle superposition still part of quantum mechanics?

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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3answers
84 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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20 views

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

I understand that from the Born interpretation that $|\Psi(x)|^2$ and $|\Psi(p)|^2$ can be interpreted as the probability density for finding a particle at x or with momentum p respectively and as ...
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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
890 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
412 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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6 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 ...
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20 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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25 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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37 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
44 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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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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11 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 ...
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1answer
25 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 ...
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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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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 ...
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1answer
100 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
86 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
52 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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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
46 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
194 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
176 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
50 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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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
24 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 ...
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1answer
138 views

Do I need to consider the spin of electrons when they are in infinite potential well

This is the problem I have And this is one of my books tell me what should I do And my question is: Do I need to consider spin in this case?(that is, I don't think the book is right...) I found ...
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0answers
36 views

De-broglie wavelength [on hold]

The de-broglie wavelength of an electron emitted from the ground state of an H-atom after the absorption of a photon equals 1/2 of the de-broglie wavelength when it is in orbit. The energy of the ...
2
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0answers
33 views

In what circumstances, can exchange interaction acquire temperature dependence?

Heisenberg exchange interaction (sometimes called as magnetic stiffness?), originating from the Coulomb interaction and the Fermion statistics, is widely used in theories of magnetism. Conventionally, ...
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20 views

What frequencies is radation being emited in infinite potential well

The problem that I am working on is. Consider an electron in an infinitely deep one-dimensional potential well of width 1nm . This electron is prepared in a state that is an equal linear ...
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6answers
433 views

Can quantum entanglement be simulated on a digital computer to any degree of precision?

First principles modelling of physical phenomena has been very successful in physics. The largest limitation is perhaps the fact that many QM problems are NP hard so we would need really powerful ...
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3answers
210 views

A modified Stern-Gerlach apparatus devised by Feynman for a thought experiment

I was revising the chapter Spin One in Feynman's lectures. There he considers a somewhat modified apparatus of the Stern-Gerlach type for convenience in explanation in the later parts of the lecture. ...
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1answer
471 views

Difference: Fermi wave length vs. phase-breaking length?

I am reading a quantum transport book, where they often mention: phase breaking length and Fermi wavelength. I have looked up and found that: Phase breaking length= length over which electron remains ...
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2answers
99 views

What is the opposite of quantization?

Is the opposite of quantization just taking the limit $h \rightarrow 0$ ? Or are there more steps involved (maybe related to bosons and fermions?)? How would one call the the opposite of quantization? ...
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1answer
128 views

Probability and double slit

if a beam of identical particles at random distances from each other (or exactly 1/2 lambda between each other) travelling with the same v towards a double sllit do not interfere with each others wave ...
8
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1answer
127 views

Bohr on wholeness?

I vaguely remember that it was Bohr who insisted that in a quantum experiment the whole experimental situation (but excluding the classical preparation and detection devices) must be considered as a ...