Tagged Questions

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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15 views

Solving of one dimensional potential sets [on hold]

is a set of 1D potentials which i need more examples and their solutions containing transmitting states, bounded states, scattering states and coefficients. I searched with 1D potential ...
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0answers
25 views

Quantised Angular Momentum?

So when learning about the Bohr model of hydrogen and de Broglie waves, it was shown that treating the electron of hydrogen as a de Broglie wave results in the relationship $$L=n\hbar$$ However, when ...
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22 views

Quantum mechanics, operator commutes with Hamiltonian

My textbook said, if an operator $\hat{O}$ commutes with the Hamiltonian, then we can use the eigen vectors of the Hamiltonian as a basis of the Hilbert space, then express the operator $\hat{O}$ in ...
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12 views

Can we calculate L-S coupling without Dirac equation?

It is known that there exists an orbital and spin angular momentum coupling for an electron moving in the atom. And the Hamiltonian can be directly derived using Dirac equation. I want to use a ...
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1answer
24 views

Using the force law to obtain total energy of an electron as a function of its radius

I am working on a problem which starts saying determine the total energy of a hydrogen atom with an electron moving with momentum $p$ at a radius $r$. For that part I got: $E = \frac{p^2}{2m_e} - ...
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1answer
55 views

What is matter made of in the light of Quantum Mechanics? [on hold]

I've always wondered what matter (particles, force particles, etc.) was actually made of considering the fact that quantum mechanics has shown us that particles can actually act as a probabilistic ...
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1answer
18 views

Are muon energies quantized?

I'm working on a problem that asks: For a central charge $Ze$, obtain an expression for the radius $r_n$ of the $n$th muonic orbit. Express this as a multiple of the radius $a_o$ of the first Bohr ...
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1answer
55 views

Representations of Galilei group

Show that the operator $U(\alpha, \beta) = e^{i(\alpha \hat{x}^2 + \beta \hat{p}_{x}^2)}$ can represent the space reflection of the 1D Galilei group: $x \to -x; t \to t$. I don't really know ...
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1answer
23 views

Rotation in configuration space

Let $R_\psi$ be the rotation in configuration space around a vector $\bf{e}_\psi$ for an angle $\psi$. How is that the space rotation in configuration space have: ...
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1answer
61 views

Bosonic Schrödinger field [on hold]

When second quantizating the Schrödinger field $$\psi(r,t) = \sum_i \phi_i(r)b_i(t),\quad\mbox{and}\quad \psi^{\dagger}(r,t) = \sum_i \phi_{i}(r)^* b_i^{\dagger}(t),$$ we have the commutation ...
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1answer
29 views

Influence of applied voltage to an electron of a metal

I would like to ask what would happen to the potential well of an electron being trapped in a metal? If I apply a voltage trying to accelerate the electron out of the potential well. Would It make the ...
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1answer
40 views

Time derivative of $\hat p$ under time varying Hamiltonian

How does one show that $$ \frac {d\hat p}{dt} = \frac 1{i\hbar}[\hat p, \hat H]$$ is valid even when Hamiltonian is time dependent explicitly? I can see that this is true when $\hat H$ is time ...
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1answer
61 views

How does path integral formulation explain bound states?

It seems to me that the intuitive explanation of path integrals in quantum mechanics describes scattering processes only. You have a particle going from A to B and you compute the probability ...
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0answers
12 views

Heat dissipation of a quantum circuit of Hadamard gate and a loop

The following Q&A about reversible computing is available here. It has listed a number of practical scenarios where a reversible circuit can still be dissipating heat. Let's assume that none of ...
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1answer
38 views

To what extent can the superconducting order parameter be thought of as a macroscopic wavefunction?

I know that the order parameter does not obey the Schrodinger equation; it instead obeys the Ginzburg-Landau equation. However, I am unclear as to the situations under which the view of the ...
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2answers
77 views

Is a wave packet physically realizable as a Fourier series?

In QM a wave packet is modeled as an infinite, or almost infinite, Fourier series, and the Fourier transform provides a transformation between momentum space and position space. To what extent is ...
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0answers
43 views

validity of Kramers-Kronig relations for all systems

Are Kramers-Kronig relations valid for all physical systems that obey causality? I came across this example http://journals.aps.org/prb/pdf/10.1103/PhysRevB.83.165119 where the authors say that though ...
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0answers
9 views

Equation of motion for Rabi resonance method

I am reading this article about Rabi and Ramsey resonance measurement, and I have trouble understanding what happens with the magnetic moment $\vec{J}$ when the oscillating magnetic field is added. ...
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2answers
81 views

Can Half Lives (hypothetically) be Measured by Wave-functions?

I understand that half-lives are measured over several days/months/years of observing a certain amount of an element and seeing how long it takes to decay a certain amount, but I'm curious as to ...
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1answer
36 views

Is the scattering length definitely positive if the potential is everywhere nonnegative?

Is the scattering length definitely positive if the potential is everywhere nonnegative? Intuitively, it seems reasonable. Any rigorous proof?
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1answer
46 views

Entangled vectors in hilbert space

We consider a system of two particles of spin $\frac{1}{2}$, each described by the two-dimensional one-particle Hilbert space $\mathcal{H}$. Let $|\pm\rangle\in\mathcal{H}$ denote the eigenvectors of ...
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0answers
28 views

Many Worlds or Infinite Worlds?

Looking at the latest paper to deal with the topic: where it purports to show that QM can be recovered from the interactions of a multitude of Newtonian worlds, we have the following statements: ...
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4answers
155 views

Why the statement “there exist at least one bound state for negative potential” doesn't hold for 3D case?

Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal. However, today I'm doing a homework considering a potential like ...
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0answers
22 views

Why free electron has orbital magnetic moment?

I was about to ask why don't we use electron beam instead of atoms in Stern-Gerlach experiment, then I saw this question and my question become why free electron has orbital magnetic moment...
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1answer
23 views

Applying the time evolution operator as a form of molecular dynamics

I had a kind of weird idea. In molecular dynamics, long timescale simulations (like protein folding) are a really hard problem because you can't "skip steps" of the simulation without huge ...
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0answers
24 views

Pair production and initial separation

I was looking at the wiki article on electron-positron pair production (http://en.wikipedia.org/wiki/Pair_production) and have a question. The article states that the photon energy needs to exceed ...
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51 views

Heisenberg approach of Quantum Electrodynamics

I am reading the book of Gunar Kallen "Quantum Electrodynamics" and in the Chapter VI he study the Vacuum polarization. He computes the experimental observable current ...
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1answer
22 views

Is the probability density of a finite potential well independent of time or not? [on hold]

The probability of the first excited state of a finite potential well is time independent or not? Why?
2
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1answer
214 views

Generalization of canonical commutation relation

The canonical commutation relation $$[x,p] = i\hbar$$ can be generalized to $$[p_i,F(\vec{x})] = -i\hbar\frac{\partial F(\vec{x})}{\partial x_i}, \ [x_i, F(\vec{p})] = i\hbar\frac{\partial ...
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0answers
41 views

Is a model of helium atom without electron-electron repulsion solvable analytically?

Consider the following Hamiltonian: $$\hat H=-\frac{\hbar^2}{m_n}\nabla_n^2-\frac{\hbar^2}{m_e}\nabla_{e1}^2-\frac{\hbar^2}{m_e}\nabla_{e2}^2-\frac Q{|\vec r_{e1}-\vec r_n|}-\frac Q{|\vec r_{e2}-\vec ...
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1answer
48 views

Do quantum physics apply universally at all scales? [duplicate]

Do quantum physics apply universally at all scales? Where do quantum physics apply? Does the nucleus of an atom abide by the laws of quantum physics? Like do we know the definitive/velocity ...
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0answers
31 views

Angular Momentum Operators confusion [on hold]

I asked a question earlier that now realize sort of made no sense, but that is only because I was combining a few things in my head....this is the question I meant to ask. How would you calculate ...
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1answer
51 views

Do Quantum Fluctuations happen evenly through universe?

I was wondering if Quantum Fluctuations are completely unpredictable, but do our observations tell us if these fluctuations happen evenly through space or are there regions where more quantum ...
1
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1answer
70 views

How to show that $(\xi\eta-\eta\xi)|A\rangle = 0$?

On page 49 of of Dirac's book, The Principles of Quantum Mechanics, he states A state may be simultaneously an eigenstate of two observables. If the state corresponds to the ket vector ...
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1answer
36 views

Folding of wave-vector in Band Theory of Metals

In the Kronig-Penney model in the Band Theory of Metals, we derive the energy levels as function of wave vector as shown in the figure. But my professor showed that we represent the levels folded ...
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0answers
82 views

I don't get the concept of “God plays with dice” - In what scenario is it proven that he does? [duplicate]

Does God Play With Dice? by Stephen Hawking I am no physicists, but I don't get the concept of God playing with dice. Logic shows me that the entire universe is calculated very precisely according ...
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1answer
36 views

What is the experimental support behind taking electrons as a revolving particles in E.Rutherford model?

From Rutherford we know that almost the entire mass and total positive charge in an atom are at the center of the atom and electrons in the atom revolve in orbit around this central core. But my ...
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2answers
45 views

Time-independent probability amplitudes for time-independent $\hat H$

I've been trying to work the following problem: If a system has a time-independent Hamiltonian with spectrum $\{E_n\}$, prove that the probability of measuring the energy $E_k$ is also ...
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2answers
71 views

How would you go about evaluating $\langle \psi \mid 100 \mid \psi \rangle$? [on hold]

How would you go about evaluating $\langle \psi \mid 100 \mid \psi \rangle$? I just can't seem to figure this out, and I know it isn't hard.
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0answers
33 views

In Quantum Physics would a camera count an observer that causes wave collapse? [duplicate]

Would the observation from a camera have the same effect on wave function as the observation from a living being?
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0answers
32 views

Deriving Graphene energy dispersion in tight binding model

I'm trying to get into graphene, in detail, I try to derive the elec. energy dispersion. Sadly, I am not that familiar with condensed matter QM by now, so I got some basic questions and I hope to find ...
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0answers
11 views

Time-dependent wavefunction for hydrogen molecule $H_2$ and hydrogen ion $H_2^+$ in the presense of laser field

I want to perform calculations for an electron-impact single ionization of the hydrogen molecule in the presence of a laser field. Basically, it boils down to evaluating the following integral $$ S = ...
1
vote
1answer
42 views

Is uncertainty a physical obstacle? [duplicate]

Heisenberg's Uncertainty Principle states that you cannot know the position and the momentum of a particle at the same time (I believe this is the main idea behind it). And I have read in various ...
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1answer
42 views

What does it mean that quantum teleportation can be classically simulated?

Quoting here from Quantum Computation by Neilsen and Chuang : (Gottesman–Knill theorem) Suppose a quantum computation is performed which involves only the following elements: state preparations ...
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1answer
84 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
2
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1answer
145 views

Can two electrons have the same momentum and spin directions?

I am trying to understand the Pauli exclusion principle. Here is an except from Feynman Lectures on Physics It just isn’t possible at all for two Fermi particles—such as two electrons—to get into ...
6
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2answers
116 views

Interpreting some domain issues of (potential) momentum operators

In the context of mathematical quantum mechanics, a well known no-go theorem known as Hellinger-Töplitz tells us that an unbounded, symmetric operator cannot be defined everywhere on the Hilbert space ...
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43 views

Simple questions on the symmetric eigenstate and time-reversal (TR) breaking eigenstate?

Followings are two independent questions as implied by the title: (1) Considering a quantum Hamiltonian $H$ possesses some symmetries described by a symmetry group $G=\left \{ g_1,g_2,...,g_n \right ...
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0answers
24 views

What is the physical interpretation of time-energy uncertainty? [duplicate]

I have a question. What is the physical interpretation of time-energy uncertainty?
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1answer
49 views

Proof of inability to obtain global phase

I'm curious if there's a quick proof of the inability to obtain global phase from a quantum state, since they're supposedly indistinguisable. I suppose to measure this, you would need a Hermitian ...