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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WKB approximation in two dimensions

Does anybody know how to implement the WKB approximation for the two-dimensional Schrodinger equation with a harmonic oscillator potential: $\frac{1}{2}\Biggl[-\biggl(\frac{\partial^2}{\partial ...
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68 views

Does quantum entanglement imply the existence of a non-causal structure connecting space-time together?

In contrast to a "time-like" or "causal" structure connecting space-time together, Does quantum entanglement imply the existence of a "space-like" or "non-causal" structure holding space-time together ...
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57 views

Proof involving the fine-structure Hamiltonian of the Hydrogen atom

Given the perturbed Hamiltonian of the Hydrogen atom: $$ ...
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41 views

Proving that Measurement increases von Neumann entropy

Let $V$ be a finite dimensional complex inner product space. Let $\mathcal{M}$ be the classical sample space of measurement outcomes that may occur in a given experiment, and $M_\mu$, $\mu \in ...
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35 views

Self-adjoint extensions with 'teletransporting' boundary conditions

When choosing a self-adjoint extension of a Hamiltonian, in general one can obtain domains in which (i) the probabilities teleport* between points on the boundary and (ii) boundary conditions ...
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29 views

Can the Berry Connection be derived from a metric?

The Berry Connection is $$A_\mu(R)=-i \langle \Psi(R) |\partial_\mu \Psi(R) \rangle$$ which allows us to parallel transport a state indexed by $R$. We can integrate the Berry Connection to get the ...
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50 views

Relationship between the Black-Scholes model and path integrals

This question was inspired by some interesting comments by Rod Vance on this answer: Minkowski spacetime: Is there a signature (+,+,+,+)? Could you (Rod), or someone else, expand on these comments ...
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66 views

Probability density of Klein-Gordon equation

This may, perhaps, stir some healthy debate; at least I am having some "fun" thinking about it, hopefully I can solicit some outside views too. It is often regarded that the Klein-Gordon equation ...
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38 views

Electron momentum distribution and wavefunction in momentum space

Does there exist any relationship between the electron momentum distribution used in above threshold ionization and the wave function in momentum space? In other words, starting with the wavefunction ...
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32 views

How to load Bose-Einstein Condensates into an optical lattice?

In cold atom experiments, what techniques are used to load Bose-Einstein Condensates into an optical lattice??
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38 views

superposition versus statistical mixture interpretation

I have an interpretation problem here. It is about the coherent state $$\left|\left.\alpha,\frac{\pi}{2\Omega}\right.\right\rangle = ...
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38 views

Young Tableuax for $SU(3)$ representations vs. $j=1$ objects

I'm working through Sakurai's Modern Quantum Mechanics and in the section on Permutation Symmetry and Young Tableaux, he mentions that a tableau constructed of $\square = ...
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48 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 ...
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45 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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49 views

Literature on the time reversal operator

Time reversal symmetry seems to be a very useful concept and is mentioned in a good number of papers I recently came across. Most of the time people claim that a certain system or Hamiltonian is time ...
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59 views

Classical/ Quantum mechanical view of magnetic monopoles

Is there any classical/ quantum mechanical proof for the non-existence of magnetic monopoles? Or is it just lack of experimental evidence that has led us to the conclusion that monopoles do not exist, ...
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113 views

What are you studying when you study a Harmonic Oscillator in QM?

This probably is a naive question - so please forgive a self-studier. In the text I am studying, one builds a HO by placing a particle in a potential that increases quadratically from the origin. The ...
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53 views

When can I use semiclassical approximation?

I know that I can use semiclassical approximation for path integral approach (in quantum mechanics) $\int d[q]e^{iA}$ when action $A >>1 $. But how shall I use such condition? For example, ...
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85 views

Different hamiltonians for quantum harmonic oscillator?

The Hamiltonian for a classical simple harmonic oscillator is $$ H = \frac{p^2}{2m} + \frac{1}{2}m\omega^2x^2$$ With the usual choice of the ladder operators $$a = ...
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52 views

Help with 1D and 2D density of states

I am currently looking at changes in DOS when sampling recipocal space finely. More precisely, I am looking at the expressions $$\rho_\text{1D}(E)\text{d}E = \frac{m}{\pi \hbar} \sum_i ...
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46 views

What are the parameters for Pauli's repulsion pseudo-force?

I have found the following formula for the repulsion potential due to the overlap of the electron clouds arising from Pauli's exclusion principle: $$V = A\exp(-r/\phi)$$ where r is the distance ...
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90 views

Solving the Schrodinger equation with appropriate symmetry

In the paper Markov Fields by Edward Nelson the introduction section claims that analytically continuing a Markov process with appropriate symmetry properties yields the solution of the Schrodinger ...
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102 views

Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
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59 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
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49 views

Physical consequences of non-trivial quantum states homology

The set of quantum states of a finite dimensional system is a complex projective space, whose homology groups are non-trivial http://en.wikipedia.org/wiki/Complex_projective_space#Homology. Has this ...
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99 views

How symmetry is related to the degeneracy?

I have several questions about symmetry in quantum mechanics. It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a ...
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49 views

Is there any connection between “Lagrangian and Eulerian formalism of fluid” and “Heisenberg and Shrodinger picture”

Is there any connection between "Lagrangian and Eulerian formalism of fluid" and "Heisenberg and Shrodinger picture of Quantum mechanics"? Thanks!
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61 views

Electromagnetic force interaction

As far as I know, the electromagnetic force only interacts on particles with electrical charge, but I was told that the electromagnetic force was involved in the following reaction: ...
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50 views

Spatial profile for a superconducting qubit's wavefunction

What is a spatial profile for a wavefunction of a superconducting qubit (such as say a flux qubit, charge qubit, or a transmon)? I am trying to calculate the energy shift of an superconducting qubit ...
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28 views

What is weak coupling of photon polarization to a pointer?

This question is refered to those who are familiar with the concept of weak measurement. In short: How can the polarization of a photon be coupled to the position of a pointer state? What is the ...
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27 views

Uncertainty principle characterizing metallic bonding?

So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is: $\Delta p \Delta x = \frac{\hbar}{2}$. And ...
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35 views

How to formulate collapse in polarization subspace of a photon?

I am wondering how to describe the collapse of a photon state when it is measured in the polarization degree of freedom (say by a filter which let pass just one particular polarisation). Let the free ...
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100 views

The Uncertainty Principle and Energy Nonconservation

The uncertainty principle is listed in most textbooks and articles as $$ \Delta E \Delta t \geq \frac{\hbar}{2}.$$ This can be derived in many ways in many different settings, most of them involving ...
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61 views

Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
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20 views

Quantum computing records (storage times)

Long storage times for qubits will be integral in the construction of a scalable quantum computer. This leads me to ask the current state of affairs in our ability to store qubits. Namely, what is the ...
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150 views

Why do some terms vanish in first-order perturbation theory?

In first order perturbation theory, we usually express the first order perturbation in the eigenket of the perturbed Hamiltonian in the basis of the unperturbed Hamiltonian $H_{0}$: ...
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69 views

leaving 2-norm propelled probability implications

I am curious about why there are no further generalized probability structures used in Physics. The great revolution was moving away from one-norm system to a two-norm system. What happens if we ...
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97 views

Derivation of existence of energy band gap in semiconductor (solid State)

I am looking for both a mathematical and a physical reason for energy band gap in metals. For Physical reason, I was told that at each reciprocal lattice, you could have Bragg scattering, that would ...
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23 views

Two identical particles with spin $s$. What is the spin of its corresponding “center-of-mass” and “relative” particles?

Consider a system of two identical quantum particles with spin $s$ and mass $m$. Using center-of-mass coordinates one obtains an equivalent system given by a particle of mass $2m$ and one of mass ...
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129 views

Does limit $\hbar \rightarrow 0$ in Quantum Mechanics mean anything?

Assuming that I learn Quantum Mechanics first, and then I approach Classical Mechanics as a special case of Quantum Mechanics, I will definitely find the relationship between Quantum Mechanics and ...
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66 views

de Broglie formula inconsistency

I recently stumbled across a small peculiarity I don't understand: According to de Broglie, the frequency of a matterwave can be written as $f=\frac{E}{h}$, and its wavelength as $\lambda = ...
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81 views

physical intuition behind quasi-bound state formation in feshbach resonance

In Feshbach resonance, by scattering theory formalism it is found that the resonance in cross-section happens when bound state energy of the closed channel is near to the scattering state energy of ...
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35 views

how is feshbach resonance potential term physically produced?

In Feshbach resonance model, a 2*2 potential term with space dependent diagonal and non-diagonal terms is written $\left(\begin{array}{cc} V_{11}(\mathbf{r}) & V_{12}(\mathbf{r})\\ ...
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83 views

Momentum representation of a state

I am trying to figure out the momentum representation of the state which has the properties $$\langle \psi |\hat q |\psi \rangle=-q_0,$$ $$\langle\psi|\hat p|\psi \rangle=p_0, $$$$\Delta q\Delta ...
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53 views

Reflector Klystron and Isolator for ESR/EPR Experiment

I am doing a lab on ESR/EPR, and I would like to know how the reflector klystron operates. It is very old and the company who made our model does not exist anymore and there are no operation manuals. ...
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87 views

What are the assumptions behind “term symbols”?

In multi-electron atoms, the electronic state of the optically active "subshell" is often expressed in "term symbols" notation. I.e. $^{2S+1}L_J$. This presumes that the system of electrons has ...
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117 views

Understanding the algebra associated with an implicit potential

In the paper here(page 7-8) the authors make a claim that the Natanzon potential (an implicit potential) follows an $SO(2,2)$ algebra. This potential defined as : $$ U(z(r)) = ...
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67 views

Motivation of the Heisenberg model of ferromagnetism

In the Heisenberg model of ferromagnetism the atoms are assumed to be arranged in a lattice. The $i$-th atom has a spin operator $\vec S_i$ (here $i$ belongs to the lattice). The Hamiltonian is given ...
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47 views

What is the difference between Lehmann-Kallen and Dispersion relation?

I know that the Lehmann-Kallen (LK) form of an operator concerns just that, an operator. But the LK is very similar in form to dispersion relations found in analytic S-matrix theory.
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79 views

Geometric quantization in Kepler problem in hydrogen atom

Why in the usual geometric quantization calculation the dimensions of eigenspaces is wrong (we can see this obstacle for Kepler problem in hydrogen atom). Here is a refference see