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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Why is Planck's constant the same for all particles?

This question came to me while reading Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from? This question has a nice answer that explains that wave number has be ...
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3answers
68 views

Constants of motion in quantum mechanics

What is the meaning of a constant of motion in quantum mechanics (an observable-operator that commutes with the Hamiltonian) in contrary with classical mechanics?
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0answers
31 views

How does a Bell measurement physically look like?

I do know how Bell states look like. They can be distinguished by doing a Bell measurement. A measurement has 4 possible outcomes (as there are 4 states, which form orthonormal basis). However I have ...
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0answers
33 views

I have a problem with the variational method approximation in quantum mechanics. Is my issue valid, or am I misunderstanding something?

The variational method for approximating the ground state of a Hamiltonian $H$ by providing a lower bound is simple enough. If we construct any test wave function $|\bar{0}\rangle$ then the claim is ...
4
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1answer
54 views

Representations of Lie group symmetries on Hilbert space

I have some troubles understanding Hilbert representations for (eg) the standard free quantum particle On the one hand, we can represent Heisenberg algebra [Xi,Pj]= i delta ij on the space of square ...
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0answers
14 views

How does the Wigner-Eckart theorem rule Multipole Expansion?

I am wondering why a spin-S particle have only the term up to $k=2S$ in his multipole expansion ? It seems that the Wigner-Eckart theorem shows the relation between spin and multipole expansion but I ...
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1answer
34 views

Importance of bound states

While solving a potential well problem we get scattering states and bound states (if exist). Number of the bound states we get depends on the potential profile. What I want to ask is, what is the ...
4
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0answers
119 views

Bound states in 1D & 2D [duplicate]

Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article, arXiv:math-ph/0208011.
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0answers
25 views

Difference between apply quantum gate and measure a qubit?

When you apply a quantum gate, why does the superposition state not collapse? Does this in any way intervene with the qubit as in the measurement?
3
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1answer
47 views

How are the PPT criterion and Bell's inequality different?

Bell (1964) writes that if we assume an equivalent classical hidden variable distribution for a two-qubit state then the expectation value of the product of two observables $A$ and $B$ can be written ...
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1answer
218 views

Wigner Threshold law in Photodetachment and Photoionization

I am writing this question here because I have a problem in understanding the Wigner Threshold law in Photodetachment and Photoionization. The Wigner Threshold Law is given by: $\sigma$=$E^{L+1/2}$. ...
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2answers
53 views

Classical notion of trajectory [on hold]

Why the classical notion of trajectory is meaningless in quantum mechanics? I am asking here about notion of trajectory from classical mechanics and why in quantum mechanics we cannot use it or is ...
3
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1answer
51 views

Evolution of Eigenstates when two spin systems are coupled

I would like to describe the following situation: We have two spin systems: Spin 1 ($S_1$) and Spin 1/2 ($S_2$). Now imagine you somehow change their interaction so that you can finetune the ...
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1answer
51 views

Do subatomic particles have dimensions?

We know atoms are mostly "made" out of empty space, so the nucleus and all the subatomic particle are very small in compared to the magnitude of the atoms. We also know that atoms are incredibly ...
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1answer
35 views

Do all quantum systems have zero point energy ?

I understand that it is possible to write an uncertainty relation between the Hamiltonian of a system and time, where the time uncertainity is defined by the amount of time it takes an arbitrary ...
0
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0answers
23 views

How do I find the electron confinement energies in a spherical quantum dot?

So if I've got a spherical quantum dot, we'll say it has a 10nm diameter for simplicity. This dot is a semiconductor and it has an electron with an effective mass altered by a factor of 0.2. How do I ...
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1answer
75 views

Quantum Mechanics Notation

Generally we have that $$|\psi\rangle=\int_{all space} \psi(\mathbf x)|\mathbf x\rangle d^3\mathbf x$$ and therefore $\psi(\mathbf x)=\langle\mathbf x|\psi\rangle$. When discussing the mutual ...
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2answers
48 views

How to verify/falsify the existence of localised edge states numerically?

I have to consider a Hamiltonian given in second quantized form in real space $$H = \sum c_k^\dagger h_{kl} c_l \, ,$$ describing fermions on a 2d hypercubic lattice. The concrete form of the matrix ...
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1answer
95 views

Slit width for minimum spot size in electron slit diffraction if involving uncertainity principle

I don't believe the following is an accurate description of the physical but a homework problem to help understanding. A beam of electron of energy 0.025 eV moving along x-direction, passes ...
0
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1answer
29 views

Normalisation of simple wave function [on hold]

I'm currently hanging on a simple normalization of following wave function: $$\psi_1(x)=N_1\exp(-\frac{(x-a)^2}{4a^2}),$$ where $N_1$ is the normalization factor to get, and $a\in \mathbb{R}$ ...
2
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1answer
58 views

Commutator of fermionic operators

The fermionic creation/annihilation operators are defined by the anti-commutation relations: $$ \{a_k^{\dagger},a_q^{\dagger}\} = 0 = \{a_k,a_q \} $$ $$ \{a_k^{\dagger},a_q\} = \delta_{kq} \, .$$ I ...
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1answer
31 views

Using creation and annihilation operators to prove the expression for the $n$th excited state in terms of the vacuum state

How does one prove that the $n^{th}$ excited state of a quantum harmonic oscillator (QHO) can be obtained by applying the creation operator $a^{\dagger}$ $n$-times to the vacuum state $\vert ...
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0answers
24 views

Strong and Weak limits in Quantum Mechanics

What are strong and weak limits in Quantum Mechanics ? especially in the terms of scattering theory and Moller operators ? References to some standard book will be appreciated.
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1answer
40 views

What is the meaning of “site”?

Reading questions, I have come across a recurring notion of "site". Whilst I am able to understand the questions I am unsure as to what a "site" actually is and to what it corresponds physically. I ...
7
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1answer
290 views
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0answers
47 views

Computing the probability density of wavefunctions

Suppose I am given a Hamiltonian operator $\hat{H}$ that satisfies the time-independent Schrödinger equation $$\hat{H} \psi = E\psi$$ I can compute energy eigenvalues and their associated ...
7
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6answers
8k views

Compton scattering vs. photoelectric effect

Say a photon hits some atom. What determines whether there will be a photoelectric effect (photon is absorbed, electron is released) or whether there will be a Compton scattering (the photon is ...
7
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2answers
982 views

Slowing down light in an opaque crystal for a whole minute

I just read about a team of physicists at the University of Darmstadt, Germany, that managed to completely slow down a beam of light that traveled through an opaque crystal (article here). How is it ...
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1answer
25 views

Physical Significance of the Planck Density

The Planck density is the Planck mass devided by the Planck volume, approximately 1093 g/cm3. Does this quantity have any known physical relevance? The Planck mass is believed to be the smallest ...
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0answers
30 views

Pion decay exercise in Griffiths books

I have questions about pion decay problem. In Griffith "Introduction to Elementary Particles" 1st edition, 1987, question number 10.10 : Analyze $\pi^-$ decay as a scattering process, using the ...
3
votes
1answer
199 views

Least Action Principle (Classical and Quantum Theory)

I) My first question would be "why should classical systems obey the principle of least action ?" When we find out the propagator in quantum physics, we find the amplitude to be equal to the sum over ...
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1answer
137 views

Are the authors saying that the observer effect plays no role in Bohr's thought experiment of the Heisenberg uncertainty principle?

Here is an excerpt from Eisberg & Resnick's Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Here is introducing Bohr's though experiment to establish a physical origin for the ...
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2answers
63 views

Are matter waves (de Broglie) classified as transverse or longitudinal? [duplicate]

We know that waves are of two types: transverse and longitudinal, and we have studied about de Broglie waves as well, so which one of them is it? Or we have other means to classify them?
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0answers
46 views

Why Position & Momentum but NOT Position & Forces involved were considered in Uncertainity Principle?

Why Position and Momentum are considered in Uncertainity Principle? What I understood is that we can predict the future state of system if we know the position and momentum of all particles ...
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0answers
46 views

What does Bell's theorem rule out?

What exactly did Bell's theorem rule out? Did it rule out "locality", so we must give up and think of Copenhagen or maybe some realism theories (Bohmian for example)? ... That's how I understand ...
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2answers
2k views

The probability of finding the electron in the H-atom

In the book Arthur Beiser - Concepts of modern physics [page 213] author separates the variables in the polar Schrödinger equation assuming: $$\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$$ then there a ...
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0answers
19 views

Are there any in depth superfluid mechanic analyses of spacetime?

Has there been much work done that treats particles as vortexes in a fluid, or dark matter as bubbles in this fluid (bending space in the same way massive particles (vortexes) are observed to do, but ...
3
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0answers
41 views

MRI and precession

A lot of explanations of the quantum mechanics of MRI discuss the precession of a proton in an external magnetic field, for example here: http://www.physicscentral.com/explore/action/mri.cfm Doing ...
3
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1answer
37 views

Bell inequality with triplet state

Is it possible to prove Bell inequality starting from a state formed from triplet states, i.e. $\frac{1}{\sqrt{2}}(|\uparrow>_A|\uparrow>_B+|\downarrow>_A|\downarrow>_B)$? If not, why? ...
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1answer
34 views

The Sturm-Liouville equations, the Schrodinger equation and the wave equation

I heard in a online quantum mechanics lecture that Schrödinger equation is an instance of the Sturm-Liouville equation and that is the super position of its stationary states gives the most general ...
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1answer
40 views

Bloch representation. Why Pauli operators?

Why do I know that a general qubit state can be written as $$ \rho = \frac 1 2 \big(\mathbb 1 +\vec r \vec \sigma\big)\;\text ? $$ It is clear that the factor of $1/2$ comes from $\text{tr}\rho=1$. ...
0
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1answer
121 views

Difference: Fermi wave length vs. phase-breaking length?

I am reading a quantum transport book, where they often mention: phase breaking length and Fermi wavelength. I have looked up and found that: Phase breaking length= length over which electron remains ...
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3answers
113 views

Can only one electron or photon produce interference pattern?

If we shoot one electron or photon at a time to a double slit for a long time, interference pattern will build up on the other side. If the gap between each electron or photon is long enough that they ...
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1answer
84 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
9
votes
1answer
610 views

What is the physical meaning of anti-commutator in quantum mechanics?

I gained a lot of physical intuition about commutators by reading this topic. What is the physical meaning of commutators in quantum mechanics? I have similar questions about the anti-commutators. ...
5
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1answer
70 views

Has anyone published the procedure to generalize ladder operators for any potential in Schrodinger's equation?

I know that the ladder operator for the quantum harmonic oscillator \begin{align} H\psi_m = \left(\dfrac{p^2}{2m}+\dfrac{1}{2}m\omega^2x^2\right)\psi_m=E_m\psi_m \end{align} is \begin{align} A = ...
0
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3answers
309 views

Is normalization consistent with Schrodinger's Equation?

Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's ...
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5answers
94 views

The nature of measurement

Does the measurement of the particle change it's physical state? Or does it only seem to do that? Ex. if a particle was measured before the slits, would we see an interference pattern, or a particle ...
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2answers
34 views

Experimental verification of bound state transition times

I am trying to reconcile, what to me at least, are two slightly different answers to what I think is the same question. The first answer below to an earlier OP implies to me that there is a definite ...
4
votes
4answers
272 views

Could dark energy be powered by force particles that obey quantum mechanics?

From what (little) I know about physics, I understand that the universe is expanding due to dark energy, and I understand that no one quite understands it yet. I also understand that the cosmic ...