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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64 views
linear response for a simple harmonic oscillator
Really sorry for this simple question, but I think it will be useful/interesting in general.
Consider a quantum simple harmonic oscillator.
Add a perturbation $H_I = -\lambda \hat{x}$
Calculate ...
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0answers
26 views
Is there anything to prevent paired-up neutrons from a complete overlap
The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions.
However, assume I ...
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0answers
38 views
exponential potential quantization
What are the energies $E_{n}$ of the Schroedinger operator
$$ -\frac{d^{2}}{dx^{2}}y(x)+ae^{bx}y(x)=E_{n}y(x) $$
for some real and positive 'a' and 'b' with the Boundary conditions $ ...
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0answers
33 views
How does a photon leave trace of its polarization state in a photon detector but not trace of which direction it came in?
Some quantum erasure experiments involve polarization of photons. In one such experiment with a double slit, a horizontal polarizer is used in front of one slit, and a vertical polarizer is used for ...
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0answers
76 views
2D quantum well energy spectrum (analytical vs numerical)
I am trying to understand the energy spectrum difference between the analytical and the approximated solution for a quantum well.
The particle is inside a box with domain $\Omega=(0,0)$X$(1,1)$. For ...
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36 views
2-body interaction energy of 3 particles
If only two-body interaction is considered then what's the energy if I put three particles on one site?
Assume delta-interaction and interaction strength is proportional to scattering length $a_F$ ...
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0answers
79 views
why is the transition $3p^53d^2 \to 3p^63d^1$ (hydrogen atom) forbidden?
What I was thinking is that in 3d subshell (l=2) we have two electrons with $$m_l=-2$$ (spin up and down)
and if we move to 3p we will fill the last vacant position - that is $$m_l=1$$ with spin down ...
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0answers
39 views
How to make DIY flight detector for double slit experiment?
I want to reproduce double slit experiment. So, is it possible to build flight detector (situated near one slit) at home? Is it possible to buy it somewhere?
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0answers
94 views
What is the height of the electron orbits of atom?
What is the height of the electron orbits an atom? (How far are the energy levels of the electron relative to the center of the atomic nucleus?)
How fast do electrons move in their orbits?
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0answers
65 views
NMR rotating frame
I'm reading about a linearly polarized field (in the context of NMR). The field is given by
$$ {\bf H_{lin}}=2H_1({\bf i}cos(\omega_zt)).$$
This can be created by having a pulse field plus its ...
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0answers
174 views
Probability and probability amplitude
What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
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0answers
97 views
How is multiplicity given by 2S+1?
Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}, l_1 = 1$ and $s2 = \frac{1}{2}, l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either +2,+1 or 0.
Now ...
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0answers
87 views
Consistent histories and Bohm mechanics, many worlds in disguise?
This was posted on here in someone's Phys.SE answer:
No, in the many worlds interpretation, every parallel universe is real, but in consistent histories, once you choose your projection operators, ...
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0answers
72 views
Showing that the Ricci scalar equals a product of commutators
I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
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0answers
159 views
Matrix manipulation for Dirac matrices
From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix}
0 & \sigma^i \\
-\sigma^i & 0
\end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix}
I & 0 \\
0 & -I
...
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0answers
86 views
Measurement in Quantum mechanics
I have got a quantum conservative system whose Hamiltonian is $H$. I consider an selfandjoint operator $O$ whose eigenvalues and eigenvectors are: $$O|\psi _{n}\rangle = \lambda _{n}|\psi ...
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67 views
How many ways are there to distribute M excitations of N identical particles among K=3 quantum harmonic oscillators?
I'm trying to numerically calculate a partition function of N non-interacting but identical particles in a 3D SHO. To do this, I'd like to know the degeneracy of $M$ excitations, $N$ indistinguishable ...
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0answers
81 views
guage invariance in Laughlin's argument
In Laughlin's gedanken experiment which aims to explain quantization of Hall conductance, one takes the adiabatic derivative of the Hamiltonian with respect to vector potential. Now it seems that it ...
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0answers
72 views
Does quantum Zeno effect play role in astrophysics?
For example, do two galaxies situated in proximity reduce the atom decay rate in each other?
What happens with decay quanta escaped to infinity? Does the radius of apparent horizon effect the ...
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0answers
53 views
Calculating the error by a small change of the potential in Schrodinger equation
In $\mathbb{R}^3$, consider the time-dependent (non-rel) Schrodinger equation with the potential energy $V(\mathbb{x})$. When a small change(e.g., just a small constant $\delta>0$) of V(x) is ...
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0answers
82 views
How to calculate radiative transition rate of exciton in a quantum dot with specific dimension?
I am writing rate equations for a nanophotonic system including three quantum dots. I need to calculate that radiative transition rates of exciton in ground state in those quantum dots.
In the paper ...
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0answers
93 views
General question on aligning a quantization axis
I have a general question on how to work with quantization axis. Here is the setup:
I am looking at a single two-level atom placed at the origin $(0, 0, 0)$, which is unperturbed in the sense that ...
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0answers
66 views
about wavefunction and vector entries
I am beginer of physics and I am studying some very fundamental idea of quantum mechanics by myself. In the introducing book I am reading, there is an example to show a particle diffraced by a slit or ...
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0answers
70 views
Asking for references on the variational treatment of spin wave
My idea is the following:
We have a system with Hamiltonian $H$, and we know that there is spin wave in this system by some symmetry-breaking arguments. Now we start from the ground state ...
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0answers
138 views
Construct the Hamiltonian of electrons on a graphene sheet ( in xy plane)
Graphene is a two-dimensional material formed by carbon atoms in a
honeycomb lattice. Because of the symmetry of the honeycomb lattice, the
electrons in graphene obey a linear dispersion relation ...
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0answers
84 views
Hubbard Model Hamitonian
$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$ is defined to be a Hamiltonian for modeling quantum random walk of identical ...
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0answers
46 views
Wigner $3j$ symbols
I am trying to determine the expansion that requires using $3j$ symbols; however, I am running into some conceptual snags. First, the expansion produces symbols that have m's that do not agree with ...
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0answers
42 views
Correlation function in relaxation in NMR
I am new in this community, I am from a chemistry background. I want to know a detailed solution of a density matrix for a singlet state using the concept of spin lattice relaxation in NMR. I will ...
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0answers
37 views
Free Energy and quantum measurement
Free Energy must be expended to reset the state of an measurement apparatus. Is this statement valid in all situations? Is there a Definitive mathematical exposition?
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0answers
53 views
fiber optic second order PMD as an operator on the tensor product Hilbert space
Second order polarization mode dispersion (SOPMD) is a coupling mechanism between polarization and frequency. Take our photon to be the following tensor product:
$\psi = \int \gamma_{\omega} | ...
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0answers
47 views
QND, CSCO, decoherence and Large N limits
While trying to actually understand the difference between QND and CSCO, I went and found the relevant reference doc, Quantum nondemolition measurements: The route from toys to tools. The key example ...
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0answers
39 views
Understanding Resonance States in Condensed Matter
What exactly is a resonance state?
My understanding so far is that a resonant state appears as a large spike in the DOS of a material due to an adsorbed impurity or vacancy in the lattice and that ...
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0answers
244 views
What happens with photon when it is slowed down substantially?
In a dispersive media light's velocity can change substantially. Imagine we can slow it down to near 0 what the wave would look like?
Frequency of light does not seem to change even at v=0 (at least ...
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0answers
34 views
In heterojunction problem, how to align the energy band in presence of bias voltage
For example, SiO$_2$ barrier embeded between Fe magnet and 2-dimensional-electron-gas such as Si.
How to align the energy bands of the three materials when an electric field is perpendicular to the ...
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0answers
28 views
Random quantum systems with asymmetric Lifshitz tails?
For a quantum mechanical system with a periodic Hamiltonian (Schrödinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ ...
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0answers
137 views
What's the differences between pseudospin and spin?
It seems that they both transform as an U(2) group, but I've been told that the three components of real spin change signs under inversion while it is not the case for pseudospin.
Could someone name ...
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0answers
47 views
four boson quantum system contact interaction
I have to solve this problem. Four bosons moving in 1d harmonic potential(their spin is 0) and interacting through contact interaction defined via delta function.
Now, methods that I have to use: a) ...
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0answers
340 views
Scattering on delta function potential
Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$.
How can one show or explain that ...
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0answers
50 views
Efficiently distinguishing mixed quantum states?
Assume we know two different mixed states, p and q, and an efficient (quantum) algorithm for creating such two. Does it follow that there exists a computationally efficient method/measurement for ...
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0answers
91 views
What is better than time-dependent perturbation theory if the pointer states aren't energy eigenstates?
Time-dependent perturbation theory works excellently if the interaction is weak and the pointer states are approximately energy eigenstates. However, what if the pointer states are not remotely energy ...
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0answers
80 views
usage of partition function in some number of particles in one-dimensional axis
I just learned some introductory quantum meachnics, but not statistical mechanics, so I am curious how partition functions would be used in the following case:
Suppose there are three particles in ...
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0answers
88 views
Non-Locality and Entanglement
Let’s consider a pair of particles [with their signals] comprising an isolated system. Any change in some property of either particle is due to the signal/s received from the other. Each particle has ...
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0answers
88 views
Bohmian Quantum Mechanics diffusion
About one year ago I attended a pretty interesting seminar of Nino Zanghì on the actual state of Bohmian mechanics.
Now, during my undergraduate studies, I didn't have the possibility to take a class ...
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0answers
174 views
How to find the Green's Functions for time-dependent inhomogeneous Klein-Gordon equation?
I'm trying to find the Green's functions for time-dependent inhomogeneous Klein-Gordon equation which is :
\begin{align*}
\left[ - \nabla ^2 + \frac{1}{c^2} \dfrac{\partial ^2}{\partial ...
1
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0answers
61 views
Unitarity and quantum cosmology
By studying quantum cosmology I was asking myself if the fact that the universe is expanding, so space is expanding and with it I would say that phase space is also expanding, so it's a non-unitary ...
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0answers
54 views
spectral eigenvalue staircase and quantum system
in a d-dimensional system of Quantum physics , does the Eigenvalue staircase
$ N(E)= \sum_{E_{n}\le E} 1 $ determine ALL the properties of Quantum System ??
for example, let us assume that the ...
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0answers
20 views
On Bolte's semiclassical law
i have seen on internet the following, for $ E >> 1 $ the Eigenvalue Staircase can be approximated by $ N(E)= \frac{1}{\pi}argZ(1/2+i \sqrt E ) $
...
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0answers
82 views
Phonon vectors and characteristic length interpretation
Basically I have a set of vectors of unit length, $\{\nu_i\}$, describing the movement of phonons (all orthogonal to each other), $\{\omega_i\}$. Lets say I only have two atoms, $m_1$ and $m_2$. In ...
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0answers
69 views
shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula
shouldn't be the quantization formula (in one dimension) equal to
$ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ??
where the Oscillating term is just the correction from Gutzwiller trace formula or a ...
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0answers
62 views
What is an isoscalar factor?
I need to find a definition for "the isoscalar factors of 3j-symbols for the restriction $SO(n)\supset SO(n-1)$...denoted by brackets with a composite subscript $(n: n-1)$..." They are given as:
$$
...
