Tagged Questions
1
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0answers
77 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 ...
1
vote
3answers
481 views
Franck Condon Principle and Born Oppenheimer approximation
My question here is purely fundamental. I am confused with the concept in Franck Condon (FC) principle and Born Oppenheimer (BO) approximation. The FC principle is in accordance with the BO ...
1
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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: $$O|\psi _{n}\rangle = \lambda _{n}|\psi ...
4
votes
2answers
251 views
WKB method of approximation
Would it be legitimate to use the WKB approximation for a particle in a spherically symmetric Gaussian potential?
$$V(r)~=~V_0(1-e^{-r^2/a^2}).$$
I'm not sure when to use which approximation ...
4
votes
1answer
132 views
Hawking Radiation from the WKB Approximation
Reading this paper which is itself an exposition of Parikh and Wilczek's paper, I get to a point where I fail to be able to follow the calculation. Now this is undoubtably because my calculational ...
1
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3answers
140 views
In solving the hydrogen atom, how to see intuitively in advance that the spin effects to the energy spectrum can be ignored?
When the hydrogen atom is solved in QM books spin is usually ignored because its effect is to add tiny piece to the energy. My question is, is there a way to see this in advance, to see that if we ...
2
votes
1answer
97 views
Are Quantum Physics and statistical theory always the same as semiclassical approximations?
Quantum Mechanics and Statistical physics is a bit hard , could we then study only the WKB approximation ?
In the form:
replace $ \sum_{n=0}^{\infty}exp(- \beta E_{n})=Z(\beta)\sim\iint ...
2
votes
1answer
202 views
Proof of adiabatic theorem on Wikipedia
I'm having trouble following the proof of the adiabatic theorem (apparently due to Messiah) on Wikipedia.
At one stage we have:
$U(t_1,t_0)=1+{1\over i}\int_{t_0}^{t_1}H(t)dt+{1\over ...
1
vote
1answer
68 views
semiclassical exact expression (in one dimension only)
let be $ N(x)= \sum_{n} H(x-E_{n}) $ the eingenvalue 'staircase' function
and let be a system so $ V(x)=V(-x)$ and $ V^{-1}(x)=\sqrt \pi \frac{d^{1/2}}{dx^{1/2}} N(x) $
then would it be true that ...
0
votes
3answers
161 views
Light Rays that are Perfectly Parallel
I just heard this simple reasoning in a documentary film:
Light rays from distant stars are perfectly parallel.
This is pretty interesting thought. In nature, it is hard to find something really ...
4
votes
1answer
266 views
Born-Oppenheimer Approximation equivalent to Tensor-product ?
If you have a wave function $\Psi$ of a system consisting of an electron and the vibrational modes of the crystal, THEN we represent the wavefunction $\Psi%$ to be in the Hilbert Space formed by the ...
3
votes
1answer
114 views
Are energies non-transferable in the Born-Oppenheimer approximation, and when does it apply?
Adiabatic approximation or the Born-Oppenheimer approximation is used whenever the electronic motion is too fast that the electrons effectively see static nuclei and the nuclei, in turn, see an ...
2
votes
1answer
206 views
Using the Scalar Electrostatic Potential to Calculate Transition Probabilities
transition probabilites of atomic systems prone to some time-varying electromagnetic field are very often calculated using perturbation theory leading to expressions including the vector potential ...
