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 quantum-field-...

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Entangled particles information transfer

No-communication theorem forbids the transfer of information using entangled particles. But does it implies that information does not pass between the entangled particles themselves? Is there a ...
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113 views

Wouldn't the thermodynamic cost of creating alternate universes make the Many Worlds interpretation implausible?

I was thinking about the many interpretations of quantum physics, and one thing that never made sense to me was the many world's interpretation. Basically at any given moment for which something ...
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83 views

GR says that time and space are aspects of the same thing, yet there is no observable for time in QM

I understand that the topic of a time operator in quantum mechanics has come up more than a few times so forgive me if this is a repeat question but I couldn't find anything specific to my question. ...
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2answers
152 views

Eigenvalues of Hermitian operators are real and the dependence/independence of boundary conditions

Without reproducing proofs: Eigenvalues of a Hermitian operator are real (proof does not rely on the boundary conditions). The momentum operator is Hermitian (proof does not rely on the boundary ...
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1answer
50 views

Photon absorbsion through 'quantum foam' [closed]

Over the cosmological distances that the photons travel from distant sources, will 'quantum foam' have an effect on them before they reach us? *Re NASA Science News Dec 31st 2015. The effect on ...
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4answers
178 views

How would my life be different without quantum entanglement? [closed]

What would happen if for some reason quantum entanglement were suddenly turned off? By "turned off", let's say that every entangled state is immediately replaced with a separable (but still ...
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8 views

Is the q-factor equal to infinite for a quantum vibrator at its ground state?

Say, a molecule is vibrating at its ground state forever, where there is no energy loss? Saw a related question here.
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1answer
389 views

Derivation of Rashba spin-orbit coupling in tight-binding model

Rashba spin-orbit coupling Hamiltonian in free space can be written as: $H_{\text{so}}=\int d^3r \Psi^{\dagger}(\mathbf{r}) \gamma (p_{x}\sigma _{y}-p_{y}\sigma _{x})\Psi(\mathbf{r})$. I expand $\...
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0answers
63 views

Calculating Natural Broadening of Emission Lines

I'm trying to demonstrate the small effect of Natural Broadening as compared to other types of broadening (Doppler, Stark, van der Waals, etc.) and my calculations don't match the accepted values. My ...
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1answer
52 views

What is the capacity of an electron to absorb energy? [closed]

When an electron get excited we find that electron absorbs energy and jumps to the required shell. This means that electron can absorb an infinite amount of energy and can get excited to infinity ...
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1answer
58 views

Quantum Mechanics: Relate solutions for two dual hamiltonians?

Consider a Hamiltonian in quantum mechanics: $$H_x=-\frac{d^2}{dx^2}+V(x,c)$$ where $x\in\mathbb{R}$ and the potential $V(x,c)$ depends on position $x$ and a continuous parameter $c$. Furthermore, ...
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1answer
41 views

Distributive property of the time-ordering symbol

Most derivations of the LSZ reduction formula, e.g. Srednicki (equations 5.13, 5.14, 5.15), Schwartz (equations 6.17, 6.18, 6.19), Wikipedia use a property of the time-ordering symbol that looks like ...
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58 views

Relation between coherent states [closed]

Suppose $\left|\alpha\right\rangle$ and $\left|-\alpha\right\rangle$ be two coherent states. Is there any relation between them or are they completely different coherent states?
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189 views

Why does $\Delta x \Delta p_x$ increase linearly with $n$ for stationary states?

Harmonic Oscillator $\displaystyle \Delta x\Delta p_x = \hbar \left(n+\frac{1}{2}\right)$ Particle in a box $\displaystyle \Delta x\Delta p_x = \frac{\hbar}{2} \sqrt{\frac{n^2\pi^2}{3}-2}$ ...
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1answer
139 views

Modern interpretation of wave-particle duality

As far as I understand, in the early days of quantum theory there was quite a lot of debate over how to interpret what it meant for a quantum mechanical object to exhibit both wave-like and particle-...
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187 views

Experiment that demonstrates the wave-particle duality of electrons

EDIT : You're about to read the first iteration of my question which is flawed. Please go to the end to see an illustration of what I meant to say. The phenomenon I was talking about is called ...
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15 views

expectaction value of coordinates on bloch sphere under special time evolution

We consider an example in which the time evolution of a system is given by the following density matrix $\rho(t)=\frac{1}{a_0+c_0}\begin{pmatrix} \eta^2(t)a_0 & \eta(t) b_0\\ \eta(t)b_0^{*} &...
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2answers
84 views

Why do different vector potentials in Landau levels problem lead to different quantum mechanical ground state wavefunctions?

Consider a charged particle (electron) moves in xy plane under a magnetic field pointing along the z direction, i.e., $\vec{B}=B\hat{z}$. As a consequence, we can write down three different gauges- ...
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1answer
215 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 ...
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64 views

Landau quantization: degeneracy of first level

In some books the degeneracy of one Landau level in a two-dimensional gas of free electrons is calculated in the following way: Note: The electron spin is not considered. Number of states of a free ...
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1answer
284 views

Does the spin of a particle change if observed from an accelerating reference frame?

If we consider a spin-$\frac12$ particle at rest in the absence of any potentials, we can use the Pauli spin operators and an associated basis to describe the observable. Let's arbitrarily choose the ...
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0answers
21 views

Heuristic derivation of Schrodinger equation [duplicate]

Is there a heuristic derivation of Schrodinger equation beginning with concepts from classical physics? When I say classical I mean something at the level of an engineer.
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2answers
105 views

Does a wave function describe the motion of electrons or atoms?

I took the course of quantum mechanics a while ago. I do not quite remember all the detail on how to derive the wave function for hydrogen but I still remember the general picture. I think the text ...
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2answers
75 views

What happens to Pauli's argument (that says that there is no time operator) when applied to $X$ operator for some simple systems?

An argument by Pauli is usually referred to in the literature when it is stated that there cannot be a time operator in quantum mechanics. This argument can be found as a footnote to P63 of W. Pauli, ...
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2answers
122 views

By what logic does one come to support a certain interpretation of quantum mechanics?

I have been on Wikipedia reading up on the various interpretations of quantum mechanics. I am entering my final semester as an undergraduate and have taken a QM course, so I am familiar with the basic ...
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2answers
71 views

Bogoliubov transformation is not unitary transformation, correct?

To diagonalize quadratic term in the antiferromagnet Heisenberg model, we may introduce the Bogoliubov transformation:$a_k=u_k\alpha_k+v_k\beta_k^\dagger$, $b_k^\dagger=v_k\alpha_k+u_k\beta_k^\...
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27 views

How to define quantum chaos?

I was told that quantum chaos is just a system whose Hamiltonian's classical version shows chaotic behavior. However, I just wondering what happens when one eigenstate of this Hamiltonian evolves? ...
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0answers
24 views

Demonstration that $H\star f(x,p)$ is equal to $Ef(x,p)$ for the time-independent Wigner function [closed]

I am attempting to understand why $H(x,p)\star f(x,p)=Ef(x,p)$, where $H(x,p)$ is the Hamiltonian, $\star=e^{\frac{i\hbar}{2}\left(\overleftarrow{\partial_x}\overrightarrow{\partial_p}-\overleftarrow{\...
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5answers
3k views

What is the conserved quantity of a scale-invariant universe?

Consider that we have a system described by a wavefunction $\psi(x)$. We then make an exact copy of the system, and anything associated with it, (including the inner cogs and gears of the elementary ...
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1answer
112 views

How to calculate fidelity of a specific quantum channel?

Let $\gamma$ be a completely trace preserving operator such that $\gamma(\rho) \to (1-\epsilon)\rho+\epsilon(|\phi\rangle \langle\phi|)$. Here $\rho$ is density matrix of two dimensional hilbert space ...
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3answers
148 views

What is a degenerate Fermi gas?

In ultracold atoms, it is generally talked of a degenerate Fermi gas. What does degenerate mean here?
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43 views

Intuition for why there are quantum beats in $V$-type but not in $\Lambda$-type atoms

When calculating the emitted intensity of an excited $\Lambda$-type or $V$-type atom with a quantized field (instead of a semiclassical approach with only quantized energy levels) one finds that there ...
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2answers
276 views

What will happen if a ground state hydrogen atom is placed in a low frequency, but high intensity laser field?

Similar questions have been asked before, but this one extends the scope of interpretation and applications. Let us ask the question: What will happen if we have a laser gun that produces a high ...
3
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1answer
42 views

Using Dyson formula in Schrodinger picture

From Time-ordering and Dyson series and what I learnt, Dyson formula is used in the situation of interaction picture: $$i\frac{dU_I}{dt} = H_{I}(t)U_I$$ where $H_I(t)$ is interaction Hamiltonian ...
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1answer
23 views

Total spin of many photon thermal state [closed]

I need to find the total spin of a large spin 1/2 ensemble in thermal state: I'm trying to find a formula for $\operatorname{Tr}(S^2 \rho)$ where $\rho=\frac{1}{Z}e^{\beta S_z}$ is the thermal state ...
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4answers
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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 \text{...
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0answers
27 views

4 Photon Entanglement

I know that if you use SPDC (spontaneous parametric down conversion, which is the process in which a photon of a certain energy and frequency is converted into two entangled photons by being passed ...
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1answer
48 views

Questions About Quantum Delta Function Potentials [closed]

I didn't think that it would be possible for a wave function to get through the delta function because there is no "leakage" of the wave function through an infinite potential barrier. I can ...
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0answers
29 views

Does the Mach-Zender interferometer imply a quantum wave function

If an optical Mach-Zender interferometer that is set up with perfect interference, then at on port no light such be detected, and at the other light will be detected. A common question asked is 'what ...
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1answer
46 views

Can free particle (eg. unbound electron or proton) have angular momentum other than spin?

I am learning about parity of nucleus and (elementary) particles. For example, proton has a intrinsic parity of $+1$. However, a more general term for parity of proton is $(-1)^l$ where $l$ is orbital ...
0
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1answer
31 views

Quantum ising/heisenberg model, states representation

I am working with a hamiltonian which looks like this (Heisenberg model) I have made a program which computes this hamiltonian using Pauli matrices (spin 1/2). My working space is then the tensor ...
6
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1answer
155 views

Can photons move in parallel?

Is it possible that two photons move in parallel, on the same trajectory - having the same wavelength, but differ in phase? Is it fundamentally possible on the level of quantum mechanics? Is it ...
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0answers
33 views

Grover's algorithm - how to capture eventual answer?

I don't fully understand what is the output of algorithm: a. Is it "value Y you search exists in your input", or b. Is it "value Y you search sits in location X of input". And another question: "what ...
1
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1answer
134 views

Gaussian path integrals and convergence

The Hamiltonian path integral in quantum mechanics, for a particle with coordinate $q$ and momentum $p$ and Hamiltonian $H=p^2/2m+V(q)$, is $\int \mathcal{D}q(t)\mathcal{D}p(t)e^{i\int_0^T(p\dot{q}-\...
6
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3answers
1k views

Can we apply Schrödinger equation in Newton gravitational potential and derive the deterministic Newton's gravitation as a special case of it

We know the solutions for wave functions of a an atom of hydrogen, and the energy values as given by spectral analysis of radiation emitted by hydrogen confirms the possible energy states as predicted ...
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1answer
41 views

How to understand the electric-field operator in quantum optics?

I know the positive field operator $\mathbf{E}^{+}$ is actually an annihilation operator $a$ while the negative field $\mathbf{E}^{-}$ is a creation operator $a^{+}$. I also learned that the ...
4
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1answer
201 views

How to obtain a vector relation for the Rabi frequency?

In this paper by Golovach et al.: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.165319 there is the following equation for spin evolution: $$\langle \dot{\bf{S}} \rangle=({\boldsymbol \...
6
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1answer
146 views

Representations of SO(3) and the classification of relativistic massive particles as in Weinberg's “The Quantum Theory of Fields”

I'm reading about the classification of relativistic massive particles in Weinberg's "The Quantum Theory of Fields", and I found something that doesn't convince me. In Chapter 2, paragraph 5, having ...
3
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1answer
51 views

Ehrenfest Theorem and boundary Conditions

In what cases does Ehrenfests Theorem hold? If I look at the wavefunction of electrons in a squared box of length $L$ (with periodic boundary-conditions, $\Psi(0) = \Psi(L)$), then the solution to ...
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0answers
25 views

Emptiness of the atom [duplicate]

If the atom is actually 99.99% empty, why can't we just put our hands or things inside them?