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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How to obtain a vector relation for the Rabi frequency?

In this paper by Golovach et al.: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.165319 there is the following equation for spin evolution: $$\langle \dot{\bf{S}} \rangle=({\boldsymbol ...
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21 views

Metastable $E=0$ s-wave bound state in a spherical potential well

I am currently dealing with scattering theory. I looked up the scattering on a spherical well potential. $$V(r) = \begin{cases} -V_0 & , r \leq R\\ 0 & ,r > R \end{cases} $$ where ...
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39 views

Determining matrix elements for dipole transition

$\renewcommand{braket}[3]{\langle #1 | #2 | #3 \rangle}$ $\renewcommand{ket}[1]{|#1\rangle}$ I have an electron in a potential $ V = k r^2/2$. I am in an initial arbitrary state $\ket{0,0,n_3}$, and ...
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35 views

Why schmidt decomposition only holds for two component composite systems?

According to schmidt decomposition any pure state belonging to a composite system $AB$ can be written as $|\psi\rangle = \sum_i \lambda_i |i_A\rangle |i_B\rangle$ where $\lambda_i$ are non negative ...
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53 views

What does the universe look like at the planck length (in a drawing)?

What is an informative drawing of the universe at the planck length, to get a deeper sense of the meaning of it? For example, you see stuff like this: But that confuses you because there is no ...
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25 views

Variational principle perturbation

I am trying to learn 2D SHO and free particle variational principles. However, I came across a perturbation like so: $Ax^2y^2$. The particle is simple harmonic in $x$ and a free particle in $y$? I'm ...
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18 views

Second-order correction in Quantum-Confined Stark effect

In the wikipedia article, there is a second-order correction in the Quantum-Confined Stark Effect. I could not understand how it was solved. I did not understand the meaning of 2(0) and 1(0) and how I ...
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36 views

Quantum Monte Carlo for harmonic oscillator

I'm trying to calculate harmonic oscillator using quantum monte carlo (path integral and metropolis algorithm). It's one particle in harmonic potential. I know the theory. One divides the partition ...
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35 views

Why don't wavefunctions for electrons in neighbouring molecules overlap?

I've come across this picture of two linked molecules. The intramolecular distances look similar to the intermolecular distances and it seems like that will be the case however you draw it because of ...
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45 views

When trying to see what symmetries an operator generates, how do you “decide” what coordinate to apply it to?

Suppose I have $\hat{O}_{1}=-i\hbar\partial_{x}$ then \begin{eqnarray} e^{-i\gamma\hat{O}_{1}/\hbar}x\,e^{i\gamma\hat{O}_{1}/\hbar}=x+\gamma \end{eqnarray} and \begin{eqnarray} ...
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29 views

What is the reason for 2 qubits no longer being entangled after interaction with a causality violating qubit?

Background : I was reading the following paper on closed timelike curves ( CTC ) : Quantum Mechanics Near Closed Timelike Curves. The Deutsch consistency equation for CTC is $$\rho_{CTC}=Tr_{CR}( U ...
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34 views

Ladder Operator proof

I was wondering what the proof was that a ladder operator will generate all the eigenenergies for a system. e.g. the QM harmonic oscillator. So after manipulating the ladder operator we get; ($a$ is ...
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23 views

How do I know the limit for the calculation of normalized wave function.

Let we have a eigen function for dumbbell ball given which is $ \phi= A e^{i x}$ and I have to determine the normalization constant A. I know in thios case I will have to write $$\int \phi \phi^* ...
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36 views

What is the equation for the pressure at which neutrons can no longer be supported by neutron degeneracy pressure?

What is the equation for the pressure at which neutrons can no longer be supported by neutron degeneracy pressure? At which point they would collapse into each other. There seems to be one for ...
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15 views

How to count total spin degeneracies for many spin one half particles?

Given the spin operator for particle $j$ \begin{align} \bar{S}_{j} = \left( \bigotimes_{k=1}^{j-1} I_{k} \right) \otimes \left(\tfrac{\hbar}{2}\bar{\sigma}\right)_{j} \otimes \left( ...
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30 views

Intuition behind modeling quantum impurities as two-level systems

I've been trying to get a basic understanding of quantum impurity problems, starting with the Anderson model. The Wikipedia article (along with some review articles) seems to explain the simplest ...
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61 views

Deriving effective model without integrating out degrees of freedom in path integral formalism?

In path integral formalism of quantum field theory (particle physics or condensed matter), one can in principle integrate out part of the degrees of freedom so as to attain an effective model ...
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Classical limit and generalized coherent states

In quantum optics coherent states introduced by Glauber have a localized probability distribution in classical phase-space with maximum following classical equations of motions. This is not a ...
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45 views

Quantum mechanics question in derivation of Heisenberg-Euler Lagrangian in Schwartz “QFT” notes

In http://isites.harvard.edu/fs/docs/icb.topic1246957.files/IV-9-EffectiveActions.pdf (Page 20) Schwartz derives the Heisenberg-Euler Lagrangian using Schwinger's proper time method. To do so, he ...
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77 views

Phenomena in the intersection of general relativity and quantum mechanics

I am looking for physical phenomena that have aspects involving both general relativity and quantum mechanics. The only example I know is Hawking radiation. While black holes are objects that cannot ...
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41 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 ...
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36 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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37 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 ...
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27 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 ...
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44 views

Schrodinger eqn with 'rescaled' Hamiltonian

If $U_t$ (time evolution operator) is the solution to the following Schrodinger equation for a time dependent finite dimentional quantum system: $\frac{d U_t}{dt} = -i H_t U_t$ can the solution to ...
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47 views

Degeneracy of Rotational Energy Levels of a Diatomic Molecule

To derive the energy levels of a diatomic molecule (with the z axis the axis of symmetry of the molecule), we write the Hamiltonian as ...
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52 views

Realism vs. locality in EPR/Bell arena

I understand that this is a much debated issue, so I will try to be precise in order to narrow the question. Bell inequality violation rules out Local Realism. From this, I understand that by giving ...
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40 views

Rotational Spectrum of a Diatomic Molecule

The rotational energy levels of a diatomic molecule are given by $$E_l=\frac{\hbar^2}{2I}l(l+1)$$ where $l$ is an integer. If the molecule is a dipole it can emit or absorb electromagnetic radiation ...
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62 views

Why is the electric field operator normalized by a volume?

I came across the following definition of the electric field operator: But I am not sure what this $V$, the "volume of a box", is about. It seems to enter the discussion in order to have standing ...
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34 views

Principle behind Atom Interferometry?

In Laser Interferometry, you propagate a laser beam, split it into two different paths, reflect once, combine it back and deduce the phase difference accumulated from the path difference, from the ...
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42 views

Do interaction free experiments violate Quantum Physics?

Although I know that interaction free experiments come under Quantum Physics, Don't the kind of violate the Heisenberg uncertainty principle? Because you get a value without interacting with the ...
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37 views

A question on intermediate step in deriving gravitational anomaly by Fujikawa's method

In Fujikawa's 'Path integrals and Quantum Anomalies', Eq.(10.26) in the derivation of gravitational anomaly in Chapter 10.1 is puzzling for me. ...
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25 views

What are the reactions that take place inside battery at the quantum level?

I was just studying about how a battery works on the internet and found out that there are reactions of chemicals which make the electrons move. But what exactly happens inside a battery (lets take a ...
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69 views

How can we prove this system is in a stationary state?

I'm having trouble using the given hint to solve the problem. The problem statement is as follows: At instant $t=0$, the probability distribution of a particle under a potential $V(x)$ is ...
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11 views

Stress testing Quantum Uncertainty, a multi Phase Question

I start this line of thinking, and i begin to seek the right questions to ask. I am of humble origin, but even here i remember that all start small somewhere. I think that even the greatest minds ...
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30 views

What is the “life time” of a trapped electron?

What does it mean for an electron trapped in a quantum well to have some life time? From the context it sort of times that the electron will move out of this quantum well at some time $\tau$ later. ...
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is there any molecular transition which emits a photon in certain direction

i know molecules having magnetic moment would be aligned in certain direction but do they emit photon in any certain direction when excited? are there any molecules which would emit photon in tthe ...
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46 views

Applicability of perturbation theory

Consider some system in some initial state $|k^{(0)}\rangle$. The probability that such a state makes a transition to some other state $|m^{(0)}\rangle$ can be computed to various orders in time ...
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38 views

Integration measure

Consider the field being decomposed into a orthogonal and completed basis: $\Phi(x) = \sum_n c_n \phi_n(x)$ (or $\Phi(x) = \int dk c_k \phi_k (x)$, if continuous) The notation: $\phi_n(x) = ...
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32 views

Minimum Uncertainty Wavepackets

I'm reading over some lecture notes on minimum uncertainty wavepackets in quantum mechanics, and I've come across a statement that I'm not entirely convinced by. My take on minimum uncertainty states ...
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74 views

Anomaly for Majorana fermion?

In 4-spacetime dimension, is there U(1) gauge field chiral anomaly associated with Majorana fermion (or I am not sure if it is equivalent, majorana representation)? Besides, I have read from several ...
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102 views

Computations for Quantum Vacuum Fluctuations

For quite some time the notion of quantum vacuum fluctuations is bothering me. What exactly is the theoretical origin of this notion? This notion has become quite common in physics and is used to ...
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46 views

Why did the universe have a low entropy at the big bang?

Sean Carroll, in his book "From Eternity to Here", asks the following question. Why did the universe have a low entropy at the big bang? in John Cramer version of the Wheeler - Feynman absorber ...
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26 views

Singular points of an orbit space

I am wondering what, precisely, the singular point of an orbit space is. Specifically, I am looking at quantum statistics and the orbit space $M^N/S_N,$ where $M^N$ is the classical configuration ...
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56 views

Simultaneous eigenket

J. J. Sakurai states in his "Modern Quantum Mechanics", this fact as a theorem ($\pi$ is the parity operator): Suppose $$[H,\pi]=0$$ and $| n>$ is a nondegenerate eigenket of $H$ with ...
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40 views

Hamiltonians on tensor product states

Solid state & Atomic Physics. The wavefunction for the electrons is $\psi(\mathbf{r}, \mathbf{R})$, where $\mathbf{r}$ is the position of the electron and $\mathbf{R}$ of the nucleus. The ...
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45 views

In Grover and Shor Algorithms 2 registers of qubits are handled at books, but it's really just one seen as 2?

I found in the literature that we require at least two quantum registers for arithmetics operation. Example: The function $f(x)=x^2$ is then a unitary evolution of the two registers, in this ...
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Do the norms of the total and the orbital angular momentums commute? If yes, why is there a problem with 2p_{1/2}?

Question: For $\vec L$ the orbital angular momentum of an electron, $\bar S$ its spin, and $\vec J:=\vec L+\vec S$ the sum, do $\vec J^2$ and $\vec L^2$ commute? I assume it does: $[\vec J^2,\vec ...
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Quantum Localization

Hi every body, Could someone please give me clarification and explanation about localization, localization length and Quantum localization? All i know is that it has something to do with diffusion. ...
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23 views

Lindhard function for surface plasmon

Is there anybody that knows how to calculate the Lindhard function for the surface plasmon (between the surface of two metals of different dielectrics)? What I'm looking for is to find this function ...