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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What trajectory do particles follow in the two-slit experiment in Bohm-de Broglie theory

In Bohm de Broglie interpretation of QM particles have trajectories; in the classic two-slit experiment what trajectories do they follow, and how is the interferance pattern interpreted? Are ...
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2answers
69 views

Where does the factor of $x$ come from in this formula for expectation value?

Given the normalised ground-state wave-function: $$\Psi(x, t)=\begin{cases} \sqrt\frac{2}{d}\cos(\frac{\pi x}{d})e^\frac{-i\hbar\pi^2t}{2md^2} & \ \lvert x\rvert<\frac{d}{2}, \\ 0 & ...
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4answers
139 views

Isn't the 'slit' in a double-slit experiment also a wave?

I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the ...
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28 views

When does electron capture occur and when does positron emission occur?

I’ve been told that electron capture occurs when there isn’t enough energy to produce a positron by beta plus decay. Exactly why is this the case? Why does it take more energy for positron emission ...
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31 views

Addition of two spins

In the addition of two spins, $S_1$ and $S_2$ show that operators $S_1^2$,$S_2^2$,$S_{1z}$,$S_{2z}$ can have common eigenkets, however, operators $S^2$ and $S_{1z}$ cannot have common eigenkets for ...
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70 views
+50

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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41 views

Why do the quantum numbers take the value they do? [duplicate]

Clearly $n$ can take any positive integer value. But what is the physics and maths behind $l=0,1,...,n-1$ and $m_l=-l,-l+1,...,l-1,l$? i.e. where do these ranges of values come from? (P.S. I know ...
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20 views

Cancelling waves and preservation of energy

In quantum physics, a particle is "defined" by a wavefunction. If you would take 2 particles with the same wavefunction, and negate one of them. They would cancel each other other out. Take for ...
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2answers
69 views

The observer experiment: quantum mechanics

If an observer is needed to see something, but it is an observer that causes a quantum wave function to "collapse" into a classical state, how could we tell that the quantum wave function even existed ...
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4answers
684 views

Is double-slit experiment dependent on rate at which electrons are fired at slit?

I am a mathematician and I am studying string theory. For this purpose I studied quantum theory. After reading Feynman's book in which he described the double-slit experiment (Young's experiment) I ...
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24 views

How is it possible to combine various techniques in cold atom experiments?

I’ve been reading about laser-trapped cold atoms (6Li in particular, which is a fermion) and was amazed at the number of things to keep track of in the experiments, just to gain that degree of control ...
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72 views

Does QFT prevent preparation of an entangled particle pair as in EPR experiment?

This is the claim Tommasini makes in Reality, Measurement and Locality in Quantum Field Theory:"Two spin $1/2$ particles, A and B, are created in coincidence in a spin-singlet state, and are detected ...
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1answer
94 views

Prove: $A$ and $B$ commute, therefore functions $f(A)$ and $g(B)$ will always commute with one another [closed]

How do I / can I actually prove the relationship $[a,b]=0 \Rightarrow [f(a),g(b)]=0$ for all functions $f,g$. I'm asking because the following sentence in the solution to my quantum mechanics ...
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0answers
85 views

How can all quantum measurement statistics be seen just as projective measurements on pure states?

Let $\rho$ be the density matrix for a system and let the POVMs be $\{E_m\}$ such that $\sum_i {E_m} = I$. The probability of getting the outcome $m$ is $\operatorname{Tr}(E_m \rho)$. The source I ...
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32 views

Is communication of the wavefunction via quantum entanglement possible?

Assume two particles are entangled and separated by an arbitrary distance. Particle 1 is in a potential well of width w1. If I'm not mistaken, the wavefunction of Particle 2 correlates to the ...
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45 views

Why does not the bare interaction potential appear in the Bogoliubov theory?

They use some effective potential defined by the s-wave scattering length, but not the bare atom-atom interaction $V(r)$. Why? It is standard practice in second quantization to use the bare ...
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28 views

Solutions to time-independent Schrödinger's equation with symmetrical (even) potential [duplicate]

A problem from Griffith's Introduction to Quantum Mechanics asks to prove the following: Given a symmetric potential $V(x)$ $(=V(-x))$, the solutions to the time-independent Schrödinger's equation ...
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2answers
60 views

unitary transformation in quantum mechanics

What two arbitrary states in the same Hilbert space can be connected through an unitary transformation? And how to construct the unitary transformation? Whether is there a general answers for these ...
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5answers
160 views

Where does particle borrow energy from to tunnel?

Where does particle borrow energy from to tunnel? It is implied that particle can borrow energy and leaped over to the other side wherever that is, the shorter the gap the more energy it borrows my ...
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1answer
47 views

physical meaning of dimensionless parameter

What does it mean when there is nor not a dimensionless parameter in my model? In quantum harmonic oscillator, we don't have dimensionless parameter while in hydrogen atom case we have one which is ...
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0answers
30 views

Does the density of water ice (any form of water ice) near 0K exceed the density of water at 277.15K?

In a question brought up by my chemistry class, the most we have determined is that the stability of most forms of ice decreases as the temperature decreases. What does this loss of stability do to ...
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49 views

Maximizing particle annihilation of a certain particle type?

Is there any theoretical situation where one would be able to maximize the production of a certain type of particle? I wish to continue discussing this question: Where would dark matter be produced? ...
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1answer
64 views

What does a light wave look like (3d model)

What does a light wave look like? The only models I can seem to find online are 2D waves, they just look like sin() graphs. I have seen the models of the two components of "light waves" (electric ...
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18 views

Can the rate of branching in the many worlds interpretation be influenced?

If I understand correctly, in the many worlds interpretation, worlds branch when irreversible interactions occur, and that these interactions occur on very low-levels. Since they occur on such low ...
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35 views

Are (active vs. passive) and (covariant vs. contravariant) related?

I've only heard about the active/passive transformation distinction and the covariant/contravariant distinction in passing, but whenever I hear about both of them at the same time, people seem to say ...
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65 views

Gluons and dark energy [closed]

According to my understanding, the dark energy is something that permeates spaces. The space in between the quantum particles(say like space between a nucleus and electrons, going even more deeper,i ...
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1answer
119 views

How is Lippmann-Schwinger equation derived?

I'd like to know the derivation of Lippmann-Schwinger equation (LSE) in operator formalism and on what assumptions it is based. I consulted the Ballentine book as advised in this Phys.SE post, but I ...
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1answer
77 views

7/2 versus 9/2 for diatomic heat capacity

Question I calculated the classical heat capacity of a diatomic gas as $C_V = (9/2)Nk_B$, however the accepted value is $C_V = (7/2)Nk_B$. I assumed the classical Hamiltonian of two identical atoms ...
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1answer
32 views

Simultaneous measurement for quantum entanglement

In the simple example that we measure the spin of two entangled particles, we measure one to have spin up so we know the other has spin down. If we could (theoretically) measure both particles at the ...
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2answers
77 views

Do black holes violate the Uncertainty Principle?

If black holes have mass but no size, does that imply zero uncertainty in position? If so, what does that imply for uncertainty in momentum?
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117 views

What is the Copenhagen interpretation of quantum field theory?

I am most interested in interpretational differences due to the fact that quantum field theory is relativistic while quantum mechanics is not. By "Copenhagen interpretation" I mean a minimal ...
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1answer
44 views

Quantum force and classical limit

Today my physicist friend told me about Bohmian mechanics as an alternative way of looking at QM. He told me that in Bohmian mechanics the wave function gives rise to another fundamental force (the ...
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28 views

Photon's behavior from 1-dimensional realm to 3-dimensional realm

I know that photon's behavior can be fully analyzed (or at least a solid theoretical explanation is present, see molecular QED book) when the photon is emitted and absorbed by same dimensional ...
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2answers
94 views

How does Lorentz invariance make $(\Psi_0,J_{\mu}\Psi_0)$ vanish?

Right before equation (10.4.7) in Weinberg's volume 1 on quantum field theory, he said $(\Psi_0,J_{\mu}\Psi_0)$ vanishes due to requirement of Lorentz invariance. As I understand, this term is a ...
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29 views

Weak measurement and weak value

The concept of weak measurements (and weak values) have become popular in Quantum information community, as I can see quite a few papers in arXiv. Since I am from Mathematical background (and the ...
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2answers
107 views

What state the wave function collapses into after an inaccurate measurement?

I'm watching MIT online lectures Quantum Physics I (roughly from one hour mark in the video). The lecturer explains wave functions that describe "Stationary States" that consist of a single energy ...
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1answer
25 views

Is there any restriction on the ability to measure the full quantum state of a system without inducing backaction?

Suppose an arbitrary quantum system is in the state $ \mid \Psi \rangle $, which may or may not be a function of time. An initially ignorant obsevrer would like to figure out what $ \mid \Psi ...
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16 views

Can we use Variational Monte Carlo for degenerate cases?

Consider Simple Example of Bose-Hubbard model $$H=-J\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1) . \tag{1}$$ We can solve this Hamiltonian by Variational ...
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1answer
47 views

Physical significance of momentum eigenfunction

In an introductory textbook of Quantum Mechanics, I found the momentum eigenfunction in position space to be given as Ne^ipx/h. Where N is the normalization factor and i is root of -1. I don't ...
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47 views

What is this normalization principle called in quantum mechanics?

I searched all over the web about this: $$\left|\Psi\right> = ...
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16 views

Why is $|a,b>+ |-a,-b>$ annihilated by the ladder operator $E_{a,b}+ E_{-a,-b}$, but no other?

Ladder operators act on states $|a,b>$ by $$E_{c,d}|a,b> = |a+c,b+d> $$ Other possible ladder operators in my example are $E_{-a,b}$, $ E_{a,-b}$ or some linear combination of them. ...
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36 views

Why does a measurement on one qubit force another one into a given state in Simon's algorithm?

This comes from trying to understand the "Simon's algorithm". So we have a set of $2^n$ kets $|x_i >$ one each for $i \in \{0,1\}^n$. Each $x_j \in \{0,1\}^n$. And we have the further constraint ...
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1answer
42 views

Would infinite material cause a black hole?

If you have an infinite amount of any material(That doesn't have a critical mass to have nuclear reactions), would this matter form massive black holes that condense into an infinite black hole? Two ...
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1answer
45 views

Unitary change of X basis, shankar, quantum mechanics 7.4.9

I'm currently working through Shankar's Quantum Mechanics and am stuck on one of his exercises. In Exercise 7.4.9 Shankar would like us to show $$|\tilde{x}\rangle = \exp(ig(x)/\hbar) |x\rangle$$ ...
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30 views

How are resistivity and tunneling related?

If we consider a sandwich with three nanometric layers: conductor-insulator-conductor and apply voltage (lower than breakdown voltage) from both sides tunneling will occur. Is tunneling dependent on ...
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1answer
51 views

Angular Momentum Operators - Commutation Relations

I was going over past PGRE exam questions, and came across this one. The components for the angular momentum operator $\mathbf{L}=(L_x,L_y,L_z)$ satisfy the following commutation relations. ...
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60 views

About the definition of the spin current

People have been talking about the spin current for a while. But there is a fundamental problem. Unlike charge, or mass, spin is not conserved. Let us take the 1d spin-1/2 Heisenberg chain as an ...
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384 views

Has a double slit experiment ever been done using a track chamber or even contemplated?

I tried searches and the question has been posed in other fora, but no experiment came up. Track chambers (cloud chambers, bubble chambers , time projection chambers, solid state detectors like the ...
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59 views

Why do electrons occupy in discrete energy states?

Why can't there be any continuous energy band in an atom?
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57 views

Beam splitter in Q.M. and C.M. - Formalism

In Q.M. the beam splitter is represented by the Hadamard transform (at least if the particle is in a state $|\Psi \rangle = \left( \frac{1}{\sqrt2} \right )(|0\rangle + |1\rangle)$ ) The Hadamard ...