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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353 views
How or why is fractional quantum mechanics important?
I read about Fractional Quantum Mechanics and it seemed interesting. But are there any justifications for this concept, such as some connection to reality, or other physical motivations, apart from ...
8
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1answer
73 views
Many body quantum states analyzed as probabilistic sequences
Measurements of consecutive sites in a many body qudit system (e.q. a spin chain) can be interpreted as generating a probabilistic sequence of numbers $X_1 X_2 X_3 \ldots$, where $X_i\in ...
6
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1answer
177 views
Entangled or unentangled?
I got a little puzzled when thinking about two entangled fermions.
Say that we have a Hilbert space in which we have two fermionic orbitals $a$ and $b$. Then the Hilbert space $H$'s dimension is just ...
5
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1answer
177 views
What is the “direction” of the transition dipole moment? (Understanding Eq. 9.29, Charge and Energy Transfer 3rd Ed, May & Kuhn)
For a real vector $\mathbf{r}$, the direction is given by: $\hat{\mathbf{n}}=\mathbf{r}/\left|\mathbf{r}\right|$.
The transition dipole moment is a complex vector. How do you define its direction?
...
4
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1answer
65 views
Origin of Ladder Operator methods
Ladder operators are found in various contexts (such as calculating the spectra of the harmonic oscillator and angular momentum) in almost all introductory Quantum Mechanics textbooks. And every book ...
4
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1answer
75 views
Simple uncertaintly calculation of the center coordinates of a Landau Level
I am reading the following review paper on the Quantum Hall Effect. I am sorry for the extremely stupid question, but I have been stuck on this very easy equation for long.
In equation 2.39, the ...
4
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1answer
107 views
Why is the Wick contraction in HFB or BCS equal to a single-particle density?
I'm trying to understand how in Hartree-Fock-Bogoliubov
(HFB) or BCS theory we can write a product of creation/annihilation operators as single-particle densities under the guise of "Wick's theorem".
...
3
votes
1answer
122 views
Change of basis in non-linear Schrodinger equation
At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
3
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1answer
167 views
Wigner's friend and quantum Zeno effect
Suppose Winger's friend is placed into a black box, thoroughly isolated from the outside world.
He constantly observes an atom with a delay of some microseconds. According to Zeno effect, atom's ...
3
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1answer
204 views
Energy spectrum of a Dirac electron
How do you explain easily "The spectrum of an electron in a repulsive potential " and hence "bound state of charge conjugation" in Dirac hole theory ?
3
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1answer
148 views
Why are the equal probabilities for Bell state measurement outcomes essential for “quantum teleportation”?
I've recently been introduced to the basics of finite-dimensional quantum mechanics from a purely mathematical point of view (with a quantum-information theme to it). When discussing quantum ...
3
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1answer
218 views
Can we have non continuous models of reality? Why don't we have them?
This question is about Godel's theorem, continuity of reality and the Luvenheim-Skolem theorem.
I know that all leading physical theories assume reality is continuous. These are my questions:
1) Is ...
3
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1answer
267 views
Are black hole states completely mixed?
A completely mixed state is a statistical mixture with no interference terms, and (QMD, McMahon, pg 229):
$$\rho = \dfrac{1}{n}I$$
$$Tr(\rho^2) = \dfrac{1}{n}$$
Are black hole quantum states ...
2
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1answer
59 views
Trying to understand mixed states
I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class).
So I'm trying to ...
2
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1answer
53 views
Why does the quantum eraser seem to violate energy and momentum conservation?
In the literature of the quantum eraser experiment it is argued that the change in statistics of the system from non-interference to interference is due to the erasing of "distinguishing information". ...
2
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1answer
107 views
Aharonov-Casher effect for charged particles
All the explanations of the Aharonov-Casher effect seem to imply it only "works" for neutral particles with a magnetic moment. This seems to stem from the duality of the A-C effect with the more known ...
2
votes
1answer
119 views
Schrodinger equation in term of Fokker-Planck equation
From Wikipedia on the Fokker-Planck equation:
$$\tag{1}\frac{\partial }{\partial t}f\left( x^{\prime },t\right) ~=~\int_{-\infty}^\infty dx\left( \left[ D_{1}\left( x,t\right) \frac{\partial ...
2
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1answer
101 views
number of gravitons launched by a proton
The wikipedia article http://en.wikipedia.org/wiki/Gauge_bosons describes how in QM exchanges of gauge bosons carry force, and describes how the graviton may also be a gauge boson.
If the observable ...
1
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1answer
41 views
How do particles become entangled?
A person asked me this and I'm just a lowly physical chemist.
I used a classical analogy (how good or bad is this and how to fix?)
Basically, light has a net angular momentum of zero, insofar as ...
1
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1answer
50 views
Is the de Broglie wavelength of a photon equal to the EM wavelength of the radiation?
Is the de Broglie (matter) wavelength $\lambda=\frac{h}{p}$ of a photon equal to the electromagnetic wavelength of the radiation?
I guess yes, but how come that photons have both a matter wave and an ...
1
vote
1answer
58 views
Where is the amplitude of electromagnetic waves in the equation of energy of e/m waves?
Does the amplitude of the photon oscillations always stay constant and if it is not - what are the physical differences between the photon with higher amplitude in comparison to the one with the less ...
1
vote
1answer
53 views
double slit experiment with two opposite quarter waveplates
Consider the usual double slit experiment involving laser and a double slit and a screen. Now place in front of the left slit a quarter waveplate (let's call it QWP1) that changes a certain linear ...
1
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1answer
159 views
Two photons transition
if an atom in its ground state is coupled to an electromagnetic field it can absorb a photon if the EM field contains one with the right frequency. These transitions depends on $⟨f|H_i|i⟩$ (from ...
1
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1answer
240 views
Long Range Spin-Spin Interactions
A recent article on probing Earth's interior mentioned the potential use of a "fifth force", long range electron spin-spin interactions, as a tool in the endeavor.
Has anybody published any ...
1
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1answer
142 views
What's the average position of oscillating particles in a box with periodic boundary conditions?
Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D).
Now put a ...
1
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1answer
128 views
Minimal Kinetic energy for particle in a box
This is driving me crazy! The question goes as follows:
A proton is enclosed in a zone of length 2pm along the x-axis. The minimal kinetic energy of the proton lies closest to:
5000eV
0.5eV
50eV
...
1
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1answer
258 views
How do I find the eigenvalues for the angular momentum ladder operators?
I am trying to calculate the normalising constants for the angular momentum ladder operators but am stuck when I need to calculate expected values.
How can I find the expected values
0
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0answers
80 views
Quantum Mutual Information scaling
Wikipedia provides a simple definition of Quantum Mutual Information:
$$I(\rho^{ab})= S(\rho^{a}) + S(\rho^{b}) - S(\rho^{ab})$$
where in terms of relative information we have:
$$I(\rho^{ab})= ...
0
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0answers
204 views
Intensity of the diffraction pattern of the double slit
I am trying another approach for my last unanswered question. (Bounty still on for 3 days. Anyone? Please?) Note that this is not the same question but a greatly simplified version concerning a much ...
0
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0answers
54 views
Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
The relation
$$\psi=Ce^{i/\hbar(Et-\mathbf{p}\cdot\mathbf{x})}\tag{1}$$
satisfies the Klein Gordon equation on the mass shell, i.e. for $E^2=p^2+m^2$.
Now let's think in the reverse direction.
...
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0answers
103 views
Can experiment distinguish the basis in which a singlet state is represented?
Let $\left(|\uparrow\rangle,|\downarrow\rangle\right)$ and $\left(|\nearrow\rangle,|\swarrow\rangle\right)$ be two bases of the $2$-dimensional Hilbert space $H$.
Can an experiment distinguish ...
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0answers
69 views
Non-simultaneous measurement of the location and momentum of an electron
I know the uncertainty principle tells us that we cannot simultaneously measure both the location and momentum of a particle with a high accuracy. The usual example we find in lectures is to imagine a ...
0
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0answers
54 views
Working principle of symmetry operations of a system with given physical situations
In the book I read some explanations about symmetry of a system.
We can make an experiment using lambda particle, A^. A^ can disintegrate into one proton and one pion - A^ and proton have same spin ...
0
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0answers
103 views
Atomic Coherence(Polarization) of Two Dipole-Dipole Coupled Atoms
My question is about generalization of most simple problem in semi-classical quantum optics. Composite system of two-level systems.
single system's diagram
where atomic frequency: wab=wa - wa; ...
0
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0answers
109 views
direct conversion of heat to electric potential / current - are there theories that contradict the 'Kelvin Statement'?
In particular, William Thomson (Kelvin) appeared to be wrong about key things in physics (initially X-rays, aether, even aviation feasibility).
...
0
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0answers
109 views
State of the entangled particles at the event horizon of black hole
Looking through the article of Samir Mathur http://arxiv.org/abs/0909.1038
he assumes that the entangled particles created at the event horizon have all the state ...
0
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0answers
103 views
Question regarding the Bohm interpretation
I tryed to understand the Bohm interpretation and this is what picture appeared to me.
Please tell me if I understood something incorrectly.
All particles have definite positions and follow ...
0
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0answers
139 views
Hardy's Theorem
https://perimeterinstitute.ca/psi_portal/sites/perimeterinstitute.ca.psi_portal/files/hardyphysrevlett.68.2981.pdf
Some researchers in Bohmian Mechanics have hoped to make the theory Lorentz ...
0
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0answers
86 views
Is this a possible scenario for the teleportation of energy?
Ok, so I've been reading a paper (Here's the paper) published by a physicist named M. Hotta et al. recently and as far as I can tell with my limited understanding, the protocol for the teleportation ...
0
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0answers
151 views
How important are constrained Hamiltonian dynamics and BRST transformation as a formalism?
I am to study BRST transformations, for which I'm currently trying to understand constrained Hamiltonian dynamics to treat systems with singular Lagrangians. The crude recipe followed is Lagrangian -> ...
0
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0answers
143 views
Brillouin-Wigner perturbation theory and the useful perturbed energy
Well, when you are working with the Brillouin-Wigner perturbation theory, the corrected energy for the perturbed system, after the first order of correction, is given in terms of the unknown variable, ...
0
votes
0answers
156 views
boundary conditions
let be the operator $ -i\hbar x\frac{df(x)}{dx}-i\hbar \frac{f(x)}{2}=E_{n}f(x)$
what kind of bundary conditions can i put ?? i have tried to find a function so for every integer 'n' i get $ ...
0
votes
0answers
136 views
Bohr sommerfeld quantiztion rule and Gutzwiller trace
assuming we can evaluate the eigenvalue staircase $ N(E) $ in both manners with the Bohr-Sommerfeld quantization rule
$ N(E)2\pi \hbar = \oint _{C}p.dq $
and using the Gutzwiller trace $ N(E)= ...
0
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0answers
59 views
Is it necessary to use all solutions when calculating an expectation value in a spin state?
I'm given an spinor $\Psi$ which is solution of the Free Dirac equation, such that is an eigenfunction of $\hat{\vec{p}}$ and has positive energy. Then I'm asked to calculate the expectation value of ...
0
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0answers
310 views
Evaluating Transition probability between different states of Hydrogen atom
I am trying to evaluate the inner product $<2S_{\frac{1}{2}},F',F'_{3}|\delta^{3}(x)\sigma_{i}P_{i}|2P_{\frac{1}{2}},F,F_{3}>$ It's written in the form $<nl_{j},F,F_{3}|$ Where ...
0
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0answers
80 views
Nonablianity of Wilczek Zee Potential
Consider a hamiltonian with degeneracies of energy in parameter space $(R)$.Now the Geometric phase(Wilczek Zee Potential) will acquire a non abelian nature.
To prove the non abelian nature of Wilczek ...
0
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0answers
95 views
WKB green function
given the Green function which satisfy
$\frac{d}{dt}G(x,s)- \frac{d^2}{dx^2}G(x,s)+V(x)G(x,s)= \delta (x-s)$
for a given potential $ V(x)$ can we obtain a semiclassical WKB solution for the Green ...
0
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0answers
136 views
semiclassical approximation for the exponential sum (partition function)
for any real and positive 's' and in the sense of semiclassical approximation
is this valid ??
$ \sum_{n}exp(-sE_{n})\sim \iint_{C}dxdpe^{-s(p^{2}+V(x))}$ valid for every 's'
here simply both the ...
0
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0answers
312 views
Ground state energies with fermions of same spin?
Consider two non-interacting Fermions (half-integer spin) confined in
a 'box'. Construct the anti-symmetric wavefunctions and compare the
corresponding ground-state energies of the two systems; ...
-1
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0answers
61 views
Quantum entanglement and speed of light $c$
On the topic of quantum entanglement, Wikipedia states:
Repeated experiments have verified that this works even when the measurements are performed more quickly than light could travel between the ...
