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Questions tagged [quantum-mechanics]

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-theory tag for the theory of many-body quantum-mechanical systems.

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1answer
40 views

Question regarding radial raising/lowering operator for isotropic harmonic oscillator

I understand the symmetry structure of the 3D isotropic harmonic oscillator $H = \frac{\mathbf{P}^2}{2\mu} + \frac{1}{2}m\omega^2\mathbf{X}^2$ as follows. The energy levels are $E_N = \hslash \omega (...
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4answers
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How do “many worlds” theorists explain particle double-slit interference patterns?

In the past couple of weeks I’ve re-watched Sidney Coleman’s wonderful 1994 lecture “Quantum Mechanics” in Your Face” and Sean Carroll’s 2019 Google talk “Something Deeply Hidden: Quantum Worlds & ...
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4answers
44 views

Quantum mechanics Interference

While learning wave-particle duality of an electron I found the wave with which we associate the electron is the probability wave. Now my questions are that if that is so How do electron show ...
2
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1answer
31 views

What do you see in 'A Boy and His Atom'

A boy and his atom is a short movie by IBM animated by actually moving atoms around and using a scanning tunneling microscope to display the result. When I first saw this picture I was fascinated ...
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3answers
407 views

Schrödinger's equation - Time reversal

While reading a book about interactions I've come to this paragraph: In the Schrodinger representation, the state function satisfies the equation $$\mathrm{i}\frac{\partial}{\partial t}\phi(t,x)=H\...
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1answer
235 views

Decay of spin-1/2 particle into two spin-1/2 particles

My question is: Does angular momentum conservation considerations alone forbid a spin-1/2 particle from decaying into two spin-1/2 particles? According to this Phys.SE post, the answer seems to argue ...
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0answers
54 views

On square integrable functions

I have just begun with Quantum Physics. My question is: do all square integrable functions represent a probability when volume integrated? Or is it only the wavefunctions under Born's interpretation?
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5 views

What is the difference between a polarised, unpolarised and partially polarised homogeneous electron gas

I am reading about electronic structure. The book uses the homogeneous electron gas as a model. The book uses the terms ‘polarised’, ‘unpolarised’ and ‘partially polarised’ in relation to electron ...
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1answer
77 views

Why are numerical solutions for the Schrödinger equation necessary?

Suppose a particle in free space given by: $$\psi(x,t) = Ae^{ik(x-\frac{\hbar k}{2m}t)} + Be^{-ik(x-\frac{\hbar k}{2m}t)}.$$ Why are numerical solutions necessary in order to plot this? Why can't ...
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1answer
199 views

Symmetry Properties for Wigner 3j-symbols

I am learning about coupled angular momenta and came across the Wigner 3-j-symbols which are defined by \begin{equation} \left( { \begin{array}{ccc} j_1 & j_2 & j_3 \\ m_1 & m_2 & m_3 \...
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1answer
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Linear Polarization of Single Photon?

I've heard it said (a while ago) that we don't usually speak of a single photon being linearly polarized or unpolarized, but rather we can speak of an ensemble of photons that are linearly polarized ...
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1answer
37 views

Charge particle collisions

If a lithium $\mathrm{Li^+}$ cation falls toward a fluorine $\mathrm{F^-}$ anion slowly in vacuum, can they find a stable 'orbital'? If not an 'orbital' will they form some kind of stable two-body ...
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3answers
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Many Worlds: under which conditions does the branching happen?

I am approaching Many Worlds interpretation and I have a big question that I would like to ask you: I buy the critic moved by Many Worlds supperters to Copenhagen interpretation, saying that Bohm ...
2
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0answers
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Is linearity of the quantum state space a necessary postulate in the reconstruction of quantum theory?

This question is about quantum reconstruction. I am new to this topic, and I decided to read some papers on it. I selected some works which follow an "information-focused" approach. The authors of ...
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0answers
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Partition function of one-dimensional harmonic oscillator of non-interacting fermions [on hold]

The energy per oscillator of an isolated system of large number of non interacting fermions in one dimensional harmonic oscillator is $5hv/4$ then Entropy per oscillator is?
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Reason for quantization of angular momentum [closed]

Why does a stationary orbit mean that the electron orbits without losing energy?
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1answer
122 views

Numerical solutions for time-dependent Hamiltonian

Currently I am facing the problem to solve numerically the following equation for a double well harmonic potential: $$i\hbar \frac{\partial}{\partial t}\psi(x,t)= -\frac{\hbar}{2m}\frac{\partial^2}{\...
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3answers
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+50

How to differentiate an operator in QM?

I recently started learning QFT and the lecturer wrote down some equations for a quantum harmonic oscillator: $$\hat H= \frac{\hat p^2}{2m}+\frac{1}{2}mw^2\hat x^2$$ $$\partial^2_t \hat x=-w^2\hat x$$ ...
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1answer
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Kraus operators of a classical quantum channel

Consider a channel $\mathcal{E}: A\rightarrow B$ that maps quantum states $\rho_A\in A$ to $$\mathcal{E}(\rho_A) = \sum_i \langle i\vert \rho_A\vert i\rangle\tau_i\ ,\tag{1}$$ where $\tau_i\in B$ ...
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Commutator Angular momentum squared with position [on hold]

I have to calculate this: $[\vec{L}^2, \vec{R}]$, I've got $([\vec{L}^2, \vec{R}])_i=[\vec{L}^2, X_i]=2\hbar^2X_i$. Is it correct?
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1answer
29 views

How to find the probability of a state from non-degenerate spectral decomposition

I have just begun learning the topics of time evolution in quantum mechanics, and I'm having trouble understanding how to calculate the probabilities of certain eigenvalues of an operator at a later ...
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0answers
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How do we find a momentum space eigenfunction? [on hold]

A particle moves in a 1D potential. The potential gives rise to a uniform force field $F$; $V(x)=-Fx$. The enegy $E$ is a horizontal line. How do we find a momentum space eigenfunction? $\dfrac{\...
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1answer
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Understanding quantum mechanics [on hold]

Forgive me for this dumb question but what are matter waves of particles? are they particles being spread out in a space like waves or the particles are still "particles" but matter waves are ...
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1answer
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What happens in an infinitely long potential step when $E<V$?

In the case of a potential step when $E<V$, the transmission coefficient of the particle is zero. However, there is also an exponentially decaying wavefunction of the particle in that classically ...
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Two particle Heisenberg model with field

I'm having trouble solving a problem with a phase transition of this system. We are considering the following Hamiltonian: $$H=-J \vec{S_1}\vec{S_2}-\mu b (S_{1z}+S_{2z})$$ And I've studied it in ...
2
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1answer
116 views

Symmetric potential well different solutions

I have solved $H|\psi\rangle=E_{n}|\psi\rangle$ with $V(x)=0$ from $-a<x<a$ and $\infty$ otherwise. If I propose a solution of the form $\psi(x)=A_{n}e^{ikx}+B_{n}e^{-ikx}$ I arrive to the ...
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0answers
37 views

The expected value of $x$

How to get the expected value of $x$ in the momentum space?
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1answer
17 views

Experimental preparation of an electron plane wave with given momentum in quantum mechanics

Boiling electrons off a hot filament constitutes a preparation providing a mixed ensemble with nearly Maxwellian distribution of momentum eigenstates. To further purify the ensemble, one can let the ...
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0answers
15 views

A relation for the state of a scatteing process

I am studying the article "A Formal Optical Model", of Bell and Squires (the article is here https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.3.96) where they proof that the self-energy of ...
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2answers
81 views

What does it mean to simulate a quantum system?

What does it mean by simulating quantum system? Can I simulate Young's double slit experiment with a quantum computer? If yes, won't it violate no-cloning theorem?
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1answer
48 views

What are the energy eigenstates for a modified quantum harmonic oscillator?

Imagine a particle obeying Schrodinger's Equation with an harmonic oscillator potential modified with an additional linear potential and cut off with an infinite potential barrier at $x=0$. That is, $$...
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1answer
234 views

Relation between radio waves and photons generated by a classical current

Several questions have been posted on Physics SE regarding the relationship between photons and electromagnetic waves, and several good answers have been given. Some of those questions are listed ...
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2answers
423 views

Perturbation theory with infinite potential

I'm trying to solve an excercise that involves first order perturbation theory and an infinite potential. To ease the problem, I tried to consider an easier one dimensional model. Consider an infinite ...
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1answer
63 views

Theory that we cannot observe everything

If I remember physics class correctly, and if not feel free to correct me, there is a theory that shows that we can not observe everything. I think the example given was energy and space. So either we ...
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0answers
27 views

What is the energy associated with the degrees of freedom of a nucleus?

I am following Martin in his book on electronic structure. On page 11 he explains that we discriminate between properties of matter due to the electric ground state, and excited states. He writes ...
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1answer
42 views

Prove that the Quantum Fourier Transform satisfies $F_N(\sum_x |xr \rangle) \simeq \sum_y |y N/r \rangle $ when $r$ divides $N$

Before I start, this is a homework question, but I have spent the last 7 hours on it and gotten nowhere. I will mention what I've tried and noticed, but it's not much. At this point, I'm wondering if ...
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0answers
27 views

Energy eigenfunctions of a truncated harmonic oscillator-like potential

Assume a potential of the form \begin{eqnarray}V(x) &=& \frac{1}{2}m\omega^2x^2,~-x_0\leq x\leq x_0,\\&=& 0,\hspace{2.5cm}{\rm otherwise} \end{eqnarray} where $x_0$ is a finite ...
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1answer
117 views

Is perturbation/interaction hamiltonian in interaction theory time-dependent

Reading quantum field theory text, I am confused on regard to whether perturbation (or interaction equivalently) hamiltonian added to free-field hamiltonian is time-dependent or not. In Heisenberg ...
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1answer
40 views

Commutation relation of spin 1-system

Given the operator $T_i$ such that, $$T_i = -\frac{i}{2} \sum_{j,k} \epsilon_{ijk} \hbar (|{j}\rangle\langle{k}| - |{k}\rangle\langle{j}|)$$ Prove $[T_i,T_j] = \sum_{k} i\hbar \epsilon_{ijk}T_k$. ...
2
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1answer
213 views

How to prove the equivalence of two different definitions of $S$-operator?

I read there are two definitions about $S$-operator: The first one (e.g (8.49) in Greiner's Field Quantization) is: $$S_{fi}\equiv \langle \Psi_p^{-}| \Psi_k^{+}\rangle$$ where $|\Psi_p^{-}\rangle$ ...
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1answer
42 views

Why do lasers require at least 3 energy levels?

I don’t yet understand why 2 energy levels aren’t enough as they can still emit photons (even when B12 and B21 are equal). By the way, I’m talking about stimulated emission.
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2answers
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In a double slit experiment, does each and every photon leave a dot on the screen in the bright area?

I have read this question: Why does the photon strike at one or another place on the tape? where PhysicsDave says: All photons passing thru the slits leave a dot on the screen, this is true for ...
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1answer
311 views

What is a scalar particle?

I was studying particle physics and I saw the word "scalar particle" many times, also in books. On the internet there wasn't any thing about it. So can anyone say what is a scalar particle ?
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2answers
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How to discretize a Hamiltonian?

In the famous article Physical Review B 92, 064520 (2015), a theoretical model was proposed to realize the chiral Majorana zero mode. $$H_{\mathrm{BdG}}=\left(\begin{array}{cc}{H_{0}(\mathbf{k})-\mu} ...
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Input Output formalism for a single-sided cavity in quantum optics, all modes same direction?

I have been trying to understand the input output formalism for a cavity by reading chapter 7 of Walls and Milburn (D. F. Walls and G. J. Milburn. Quantum optics. Springer, 2006.). There is something ...
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3answers
783 views

Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$ H_1' = - \frac{p^4}{8m^3 c^2} $$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
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1answer
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Could ripples in the fabric of reality explain the double slit experiment? [on hold]

I was looking at the single photon double slit experiment and how they achieved having just one photon at a time passing through the slit: they emitted 100 photons per second(in the variant I found ...
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1answer
237 views

Barrier Potential for bound states

I'm having this problem for a while, but I'm still failing to realize what really is bothering me in this, so here is my attempt on explaining my doubt: I have the time-independent Schrodinger ...
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5answers
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Why doesn't the nucleus have “nucleus-probability cloud”?

While deriving the wave function why don't we take into the account of the probability density of the nucleus? My intuition says that the nucleus is also composed of subatomic particles so it will ...
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2answers
40 views

How should the electric field produced by an electron look like if electron is described by a wave function?

In quantum mechanics, the position of an object is not definitely known, but instead is described by a probability density function of where it would be located. Then what should the electric field ...