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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Bragg Scattering of Thermal Neutrons

I'm currently reviewing Bragg scattering. The particular problem below has me slightly confused on whether I'm thinking about it correctly. Questions Is the problem below referring to the kinetic ...
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16 views

potential decomposition in terms of Bloch eigenstate

Given a single particle Hamiltonian $H=-\frac{\hbar^2}{2m}\nabla^2+V(r)$, where $m$ is the electron mass and $V(r)$ is a periodic function representing the lattice potential. It is defined in the ...
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17answers
55k views

What is a good introductory book on quantum mechanics?

I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for ...
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3answers
67 views

What Quantum Mechanics is really all about?

This question might sound very silly, so I'm sorry if that's the case. I'll try my best to make my point clear here. Before explaining, just to make clear, I'm not confused because of the Math ...
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1answer
55 views

Dr. Pierre-Marie Robitaille: On the Validity of Kirchhoff's Law

Lately I've been researching about the black-body spectrum and the historical development of Planck's Law. I mainly wanted to understand a little bit more why many different objects (Stars, Hot ...
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1answer
18 views

What is meant by the expression “Markovian dynamics”

I know what a Markov chain is but what does it mean in physics when I say that I assume Markovian dynamics? For example in Quantum Mechanics, I read that it means that the time evolution can be ...
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2answers
257 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 ...
3
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2answers
146 views

State of a system in Quantum Mechanics and state vectors

I'm taking a course in Quantum Mechanics and there is something I'm not being able to fully understand. On more elementary courses on Quantum Mechanics I've been told that the idea of Quantum ...
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1answer
75 views

Why is a relativistic quantum theory of a finite number of particles impossible?

In Dyson's book Advanced Quantum Mechanics , he said "These two examples (the discovery of antimatter and meson) are special cases of the general principle, which is the basic success of the ...
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18 views

Perturbation theory, eigenvalues and eigenvectors for degenerate case (1st order)

I was trying to understand the perturbation theory, but I was lost in the notation... I have understood that I have to identify the imperturbed kets that are degenerated and find the matrix V, where ...
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20 views

Is there a constant decay of particles that maintains the value of the Quantum Vacuum?

By my question I am attempting to understand how the Vacuum of space remains at a constant value, (GR the universe on the large scale matches the “critical” energy density of about 8.5×10-10 J/m3) ...
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18 views

What quantum measurement formalism is easiest to implement physically?

As part of my studies and research, I have learned to work with three different measurement formalism which I define to avoid any ambiguity with the nomenclature: General measurements, which are ...
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1answer
43 views

Show that the minimum energy value for a given $l$ increases as $l$ increases

"Consider a particle in a central field and assume that the system has a discrete spectrum. Each orbital quantum number $l$ has a minimum energy value. Show that this minimum value increases as $l$ ...
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27 views

Is the universe a Turing machine?

Reading about Computable numbers I wondered if there is any physical experiment that returns non-computable numbers or if there is any physical theory that needs non-computable numbers. Because if ...
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0answers
66 views

Free probability in Physics

Recently I have started reading some materials on non-commutative probability. IN this area mathematicians sometimes consider quantum theory as a non-commutative version of classical probability, with ...
6
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3answers
124 views

How to understand the motion of a particle in Quantum Mechanics?

In Classical Mechanics when we talk about the motion of a particle it is the same as talking about the idea of trajectory. The fact is that in Classical Mechanics, a particle has a definite position ...
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2answers
67 views

Using slope=0 technique to find most likely spherical shell

In this PDF http://riedo.gatech.edu/Teaching/Modern_Physics/hw/HW3_2010_MP_SOL.pdf problem#1, the instructor solves the question of which spherical shell (what radius $r$) has the greatest ...
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0answers
16 views

A wave is passing through a potential barrier

Let assume a wave is passing through a potential barrier. Like this: What will be happened to the amplitude or the shape of the wave during the movement through the potential barrier? {assuming ...
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0answers
13 views

Repulsive potential for free fermions

My question -which is probably easy to answer for a physicist- stems from trying to understand the repulsive interaction between fermions. For instance the fact that states of multifermion systems are ...
12
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4answers
11k views

Is it possible to reproduce Double-slit experiment by myself at home?

I want to reproduce this experiment by myself. What I need for this. What parameters of slits and laser/another light source it needs? Is it possible to make DIY-detector?
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0answers
37 views

Is this solvable? Time-dependent perturbation theory

The question is A hydrogen atom is placed in a time-dependent homogeneous electric field given by $$ \varepsilon(t) = \varepsilon_0(t^2 + \tau^2)^{-1} $$ where $\varepsilon_0$ and ...
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3answers
52 views

Problem with tracing over the environment and obtaining reduced density operator

I'm reading an article by Bas Henson given here. On page 25 he deals with the double slit experiment Given the wavefunction which is his equation 1.75, he claims he has traced over the environment ...
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1answer
57 views

Lippmann-Schwinger equation and $T$ expansion

Lippmann-Schwinger equation, in operator form, is: $$ T=V+V\frac{1} {E-H_0+i \hbar \varepsilon} T=:V+V\Theta_0T, $$ where $H_{tot}=H_0+{V}$ is the hamiltonian ($H_0$ is the free particle hamiltonian ...
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3answers
591 views

Why is momentum quantized in a 1D box even though the operator doesn't give eigenstates?

We don't get eigenstates of momentum when we operate momentum operator in the wave function of particle in a 1D box problem yet we say momentum is quantized in this situation. Why is it so?
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2answers
71 views

Is there a mathematical relationship between Legendre conjugates and Fourier conjugates?

In quantum mechanics, there is an uncertainty principle between conjugate variables, giving rise to complementary descriptions of a quantum system. But the variables are conjugates in two different ...
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1answer
50 views

Completeness relations of eigenstates in the Heisenberg picture

I've been reading Srednicki's introduction to path integrals and I'm slightly unsure of the notation that he uses for the completeness relation of position eigenstates in the Heisenberg picture. In ...
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33 views

What is special about quantum entanglement? [duplicate]

Get two pieces of paper. In secret write the same number on both papers. Transfer one paper to the Moon. Look to the paper which is left at the Earth. Voila! We know what is on the Moon paper. The ...
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3answers
51 views

Can't we consider that EmDrive is Pushing against Space itself? [on hold]

When something move through space it pushes against something else in space with equal force. However, EmDrive warps space around. So can't we say it's pushing against space itself, and thus momentum ...
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0answers
38 views

What does $(I + iδH^t)(I-iδH)$ equal to? [on hold]

$I$ is equal to 1, $δ$ is a small change. According to 43:04-43:10 of this video http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter/lecture-4 \begin{align} \ i{ δ }(H^t-H)=0 ...
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2answers
111 views

Infinite square well that suddenly decreases in size

A well known exercise in basic quantum mechanics is the sudden (diabatic) increase of the length of an infinite square well. Now consider a particle in an eigenstate of an infinite well that is ...
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0answers
56 views

How to find $\langle x^2 \rangle$ of a wavefunction $\psi(x,t)$ [closed]

I know how to find $\langle x \rangle$ of such a function, but I'm not sure of how to find the variance or $\langle x^2 \rangle$ of this continuous function. Any help would be greatly appreciated. ...
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1answer
93 views

Prove that Laughlin's 3-electron states are a complete set of states

In R. B. Laughlin's 1983 Physical Review B article, Quantized motion of three two-dimensional electrons in a strong magnetic field, Laughlin separates out the center of mass motion of the electrons, ...
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1answer
39 views

Oscillation of Atom

What exactly does it mean when one says 'one atom of Caesium 137 oscillates 9,192,631,770 times'? I do understand the general thing about oscillation but what exactly is the oscillation of atom, what ...
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1answer
44 views

De Broglie's Matter wave equation dividing by zero

I was just thinking about De Broglie's matter wave equation: $\lambda=\frac{h}{p}$ where $p$ is the momentum of the object. But what if the object is at rest? Won't we be dividing by zero? What if we ...
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1answer
39 views

Meaning of expectation value of product of non-commuting operators

Let $\hat{A}$ and $\hat{B}$ be Hermitian observables with spectra labeled by $a$ and $b$. Then we can write \begin{equation} \hat{A} = \sum_a a\, \hat{P}_a \end{equation} \begin{equation} \hat{B} = ...
2
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2answers
106 views

Is there any $SU(\infty)$ gauge theory in quantum field theory?

The groups $U(N)$ and $SU(N)$ are the most important Lie groups in quantum field theory. The most popular are the $U(1),SU(2),SU(3)$ groups (these gauge groups form the Standard model). But is there ...
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1answer
213 views

spooky nonlocal communication, or bad abstract?

I'm referring to this recent paper, "Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurements" by Fuwa et al. published in Nature Communications. ...
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2answers
84 views

Can an electron go along different paths at once in a circuit

A single electron moves along a circuit and comes to a fork in the wires. The wires separate but come back together near the end of the circuit. From what I know, the electron will travel along all ...
1
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1answer
37 views

Books on waves with Fourier Transforms

There are many waves and oscillations books out there that also include Fourier analysis but very few give the subject a thorough treatment, they just pass it in a few pages. If anybody has any ...
3
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6answers
484 views

Fermion vs. Bosons and particle vs. wave: is there a link?

I'm puzzled since several years on this basic aspect of quantum mechanics. Quantum theory is supposed to describe particle-wave symmetry of our world. It also describes our universe in term of bosons ...
1
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2answers
197 views

Is entropy a meaningful concept on a quantum level?

My naive assumptions, as I really am at a pretty basic stage in QM, are as follows: Classically, entropy gives us a practical measure of the direction of time, as opposed to our physical laws which, ...
0
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0answers
41 views

What's the physical meaning of the different entanglement entropy of mixed bipartite systems?

As we know, for pure bipartite systems, the entanglement entropy are the same for both subsystems. But this is not the case for mixed states. Can anyone explain what's the physical meaning of this ...
2
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1answer
34 views

Sources to learn about Berry phases and Adiabatic Theorem

I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect. As I found them very ...
2
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1answer
130 views

Quantum fluctuation

According to the quantum fluctuation concept, a particle and its corresponding antiparticle appear out of nothing only to annihilate and emit some energy in the form of electromagnetic waves. Does ...
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0answers
28 views

How to form a density matrix? [on hold]

forming a density matrix when two independent states are there
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0answers
42 views

Can a density matrix be complex? [on hold]

Normally a density matrix is thought of as a statistical ensemble of pure states. However, after using the Time-Evolution Equation (or Master Equation) to evolve a density matrix, they start to have ...
0
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0answers
19 views

Can there be a link between non-locality and non-Markovianity?

Non-locality is a curious feature that is linked to the violation of Bell inequality of any form. It arise from the impossibility of simultaneous joint measurements of observables. The ...
4
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1answer
257 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
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2answers
89 views

Why is local realism not possible with QM?

In Mermin's thought experiment (pdf) particles are sent to two detectors A and B with 3 settings each. If the particle passes the test, we get a green (G) light, else red (R). Now in QM we could send ...
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1answer
45 views

Barycenter and relative coordinates for schroedinger equation of the hydrogen atom

Heyho, i just realized i am not sure how one gets from: $\Big(-\frac{\hbar^2}{2m_e} \Delta_{r_e} - \frac{\hbar^2}{2M_P} \Delta_{r_p} +V(r) \Big)\Psi(r_e,r_p) = E \Psi(r_e,r_p)$ to: ...