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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1answer
194 views

How are matrices used to represent quantities, and what is the meaning of a matrix?

So I'm reading this text on Quantum Mechanics, and it goes through a few chapters that I understand fairly well including probability. But then it says that all quantities, like position and energy ...
0
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0answers
46 views

Double slit experiment using 2 electrons

Suppose 2 electron guns shoot an electron at a double slit at the same time, then how do you predict for each electron the probability density of it landing at each position when the 2 electrons repel ...
5
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0answers
126 views

Could energy be stored into (not extracted from) the quantum zero point field (like a battery)?

In order to explain the question clearly, I will make a short introduction. In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to ...
2
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4answers
534 views

Double slit experiment and single particles. Is the wave function just a mathematical model?

I really do want to apologize in advance, I know this question has been 'answered' before. I have this 'problem' of feeling negatively toward much of today's 'mystical' interpretations of physics, ...
2
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1answer
78 views

What happens to electrons when they are detected?

I know photons are absorbed and annihilated when they are detected but a) when electrons are detected, are they absorbed and annihilated? and b) if electrons are ever absorbed, what happens ...
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0answers
122 views

Center of mass coordinates in Lagrangians and Laplacians

Is there a quick nice and easy way to write Lagrangian's and the classical/quantum Laplacian operator in terms of center of mass coordinates? The algebra is so involved and it has me confused about ...
3
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3answers
85 views

Which side of wave-particle duality to choose in a given situation

How does one know whether, in treating a certain problem, one should consider particles as waves or as point-like objects? Are there certain guidelines regarding this?
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3answers
243 views

Runge Kutta Method for a Lindblad Equation

I am solving a Lindblad equation for a dissipative Harmonic Oscillator. My Hamiltonian is time dependent, My Lindblad Equation can be written as \begin{equation} ...
3
votes
2answers
505 views

Integral equations contradict The Uncertainty Principle?

I was reading about Integral equations, and I found this excerpt in Portuguese Wikipedia: "integral equations serve to determine the position in all instances of an object, if known, its ...
4
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1answer
886 views

Liouville-von Neumann equation can be directly derived from Heisenberg picture?

The Liouville-von Neumann equation for the density matrix is: $$ i\hbar\frac{\partial\rho}{\partial t}=[H,\rho],$$ while in the Heisenberg picture: $$ \frac{d}{dt}A(t)=\frac{i}{\hbar}[H,A(t)] ...
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0answers
69 views

What is the eigenvalue of $J_z$?

In the calculation of the Zeeman Effect, the most important calculation is $$\langle J_z + S_z\rangle.$$ Suppose we want to find the Zeeman Effect for $(2p)^2$, meaning $l = 1$. In Sakurai's book, ...
3
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2answers
195 views

Books about alternative interpretations of quantum mechanics

Recently I've heard that there exist alternative interpretations of quantum mechanics which, while not as widespread as the Copenhagen intepretation (or so it would seem), are equally valid in the ...
1
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1answer
97 views

Manipulation with braket notation

I am still getting used to the braket notation. Is this manipulation correct? $$ \frac{-\hbar^2}{2m}\int_{-\infty}^{\infty}\frac{\partial^2\phi_n^*}{\partial z^2} \phi\,dz = ...
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1answer
118 views

Does Anything Exixts? [closed]

I Mean that Does Anything In The Universe Exists By Means Of Quantum Mechanics...I Heard This From Someone But i wanna be sure that it is really true or what?.
5
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2answers
154 views

Representation of indistinguishability in quantum mechanics

I was wondering that if particles are indistinguishable in quantum mechanics, then why do we still express their states $\left| \uparrow \downarrow \right\rangle$, as meaning particle 1 (in the first ...
0
votes
2answers
124 views

Which is the most fundamental constant between the Planck constant $h$ and the reduced Planck constant $\hbar$?

This question is related to Planck units (also called natural units, absolute units or God's units). I'm wondering which constant is the most fundamental and should be normalized to 1. I would like as ...
2
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0answers
203 views

Coherences in the density matrix

It is said that the off-diagonal elements of density matrix are coherence. When a system interacts with its environment the off-diagonal elements decay and the ...
3
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3answers
705 views

An operator on the other side of the Schrödinger equation

A form of the Schrödinger equation is $$ \left[-\frac{\hbar^2}{2m} \nabla^2 + V(\vec{r}, t)\right]\Psi = i\hbar \frac{\partial}{\partial t} \Psi $$ The bracketed term is of course the ...
4
votes
1answer
211 views

After using annihilation operator on vacuum state, why it is $0$ instead of vacuum?

For bosonic systems, why $a|0\rangle=0$ and not $a|0\rangle=|0\rangle$?
2
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1answer
37 views

Neutral quantum particle in inhomegeneous magnetic field

I'm trying to understand Stern-Gerlach experiment on a computational level. Suppose we have a neutral particle with magnetic moment (e.g. a neutron), and apply an inhomogeneous magnetic field to it ...
2
votes
2answers
98 views

Photons and Absorption

Hello and thanks for reading my question: Imagine we send one photon at an atom, and it happens to be the right frequency such that it gets absorbed fully by an electron in this atom. Obviously that ...
0
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0answers
125 views

Gutzwiller mean-field method in Bose Hubbard model

Gutzwiller mean-felid method is an efficient way to study Bose-Hubabrd model in optical lattice with a harmonic trap. Gutzwiller method assumes there is no spatial correlation within the trap, so ...
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0answers
117 views

Particle In a Box and momentum, velocity

So on a homework assignment, we are give the width of a well, $a$, and the mass of the particle $m$ and we want to find the average velocity of the particle at the n=1 state. So here is my attempt at ...
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0answers
11 views

How an-isotropic magneto resistance(AMR) changes as film thickness increases?

As the film thickness increases, an-isotropic magneto resistance(AMR) changes in the presence of external magnetic field because of spin orbit interaction. But i don't know how it is responsible for ...
2
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4answers
571 views

Why is $ \vec{S}^{(A)} \otimes \vec{S}^{(B)} = \frac{\hbar^2}{4}(\sigma_x \otimes \sigma_x + \sigma_y \otimes\sigma_y + \sigma_z \otimes \sigma_z)$?

I haven't been taught tensor product in class but they have taught us addition of spin. I looked up online in this link->http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_7.pdf#page=10 ...
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7answers
6k views

Why is it said that without quantum mechanics we would not have modern computers?

I've heard this in many quantum mechanics talks and lectures, nevertheless I don't seem to grasp the idea behind it. What I mean is, at which point is that our modern understanding of quantum ...
2
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1answer
111 views

On use of Hamiltonians for Helium

The Hamiltonian of helium can be expressed as the sum of two hydrogen Hamiltonians and that of the Coulomb interaction of two electrons. $$\hat H = \hat H_1 + \hat H_2 + \hat H_{1,2}.$$ The wave ...
2
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2answers
127 views

How does one produce entanglement?

In practice, when entangling two particles (say two electrons), is creating an entangled state purely a matter of bringing them close enough together? What I mean is, to make their wave functions ...
2
votes
1answer
416 views

Effective Hamiltonian / Perturbation theory for non-degenerate case

Trying to wrap my head around the following situation. Consider first a case that I understand well: Let's assume a three level system where the lowest two levels are degenerate and individually ...
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0answers
57 views

Deriving probability distributions from the Wigner distribution

I know that I can calculate the probability distributions of $x$ and $p$ from the Wigner quasiprobability distribution, and I can calculate the probability distributions of other operators by ...
2
votes
1answer
554 views

Particle in a 1D Box with Symmetric potential: How find solutions?

I am working on a problem in which I shall find the normalised solution to the 1D particle in a box. Solving for the particle in an asymmetric potential is quite straight forward, but I run into ...
2
votes
3answers
276 views

Do ionisation of atoms release photons?

I was reading through my text book about Fluorescence. It said "inside a fluorescent bulb, the mecury atoms collide with each other and with electrons get excited and ionised. During de-excitation, ...
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0answers
89 views

Time evolution of quantum states

Time evolution of a quantum state is fully described by a one parameter family of unitary operators. What I can't seem to understand is, given some unitary operator acting on some Hilbert space, can ...
3
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1answer
246 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
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2answers
309 views

How to determine a strong or weak interaction (Strange particles)?

As you know $\pi^-$ meson + proton ---> $K^+$ meson + $\Sigma^-$ particle. (AntiUp,down) + (up up down) --> (up antistrange) + (down down strange) I know that the quark number has be conserved in ...
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1answer
75 views

relation between photon number and energy

Suppose there are two light beams. One is red while the other is violet. The energy of both is the same. Which one of these beams has a larger number of photons, or is the number of photons relevant? ...
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0answers
105 views

Big Bang, Heat Death, and cause and effect

If the Universe has two 'end points', one being the Big Bang, and the other being heat death, is there anything in the laws of physics which forbid a random fluctuation in the heat death state from ...
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0answers
75 views

How to make a base tranformation for a linear operator in QM? [closed]

I have 2 bases A and B with the following kets: Base A: $|a_1\rangle$ and $|a_2\rangle$ Base B: $|b_1\rangle = \frac{1}{\sqrt2} \cdot(|a_1\rangle + i\cdot|a_2\rangle)$ $|b_2\rangle = ...
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82 views

Quasi-Degenerate Perturbation Theory

Is there any sort of objective rule on when to use quasi-degenerate perturbation theory vs degenerate vs non-degenerate?
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2answers
285 views

if the universe is flat does it mean it exists only in our mind as math? [closed]

My dad, who is a retired mathematician, has this attitude, which I think we all have as kids, that ultimately reality is made of stuff. End of story. If you look around yourself in the world, ...
1
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2answers
265 views

What does this quantum experiment says about quantum world?

I am complete noob so please bear with me. I always read that in quantum world things exists as probability and only become one when they are observed...or wave collapses into particle. But there was ...
3
votes
1answer
79 views

Using the fine structure constant to measure atomic and molecular sizes

This is kind of a coursework question but it bring up some really interesting things about the fine structure constant $\alpha$ so I wanted to post it to not only make sure I understood something but ...
9
votes
1answer
256 views

Interpretation of the Instanton in SUSY QM

This is a loose follow up to this question: Interpreting Argyres' spectrum of spontaneously broken SUSY QM. In SUSY QM, the Hamiltonian can be cast as a 2x2 matrix $$ H = \frac{1}{2}p^2 + ...
5
votes
1answer
163 views

Energy fluctuations in quantum canonical ensemble

How would you go about showing that in the quantum canonical ensemble (that is, in the density matrix and operator formulation), the energy fluctuations, namely $\langle H^2\rangle - \langle ...
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0answers
63 views

Is entropy a dynamical quantity [closed]

I am confused whether Entropy is a dynamical quantity or not. Gibbs entropy, and quantum mechanical Von Neumann entropy.
2
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0answers
49 views

Can someone explain to me the Rocksar-Kivelson Hamiltonian?

The following paper shows the hamiltonian of the 2D quantum dimer gas (page 2) http://www-thphys.physics.ox.ac.uk/people/ClaudioCastelnovo/Talks/050209_MIT.pdf Here are some questions I have. Why ...
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0answers
41 views

Subnuclear physics vs wave function

This question is more a philosophical question than a physics one. When we appreciate particle physics we study that in order to explain some experimental results we have to introduce a new particle ...
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1answer
187 views

Nonzero ground state energy of the quantum harmonic oscillator [duplicate]

Since $\frac{1}{2}\hbar \omega$ is the zero point energy of the ground state of the harmonic oscillator, then there is no way to extract this energy. Therefore, in what way is this value different ...
0
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1answer
116 views

Is it possible to find the hydrogen atom's radial wavefunctions?

Is there a way to actually find the equation of $R(r)$ without looking at a table with these equations already given? I'm given $n$, $\ell$, and $m$.
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0answers
99 views

Quantum Logic and Quantum Field Theory

Quantum Logic is a very interesting and powerful answer to the problem of Quantum Mechanics foundations. Nevertheless this approach is usually developed in a non-relativistic framework. Is it still ...