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2
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1answer
119 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 ...
1
vote
0answers
165 views

Hooke's Law and the shape of coils

I've learned in school that the force in a coil is $F=kx$, linear on how much the coil is stretched. Two questions: Is it always linear for every shape of a coil? Does it remain linear if we ...
2
votes
1answer
415 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
77 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 ...
2
votes
1answer
290 views

A missing factor of 2 in the standard Hartree-Fock mean field?

Let's start from a very simple argument: If $A$ and $B$ are some operators, then I can write their product as $$AB = (A-\langle A\rangle)(B - \langle B \rangle) + \langle A \rangle B + A \langle B ...
3
votes
2answers
739 views

Why are continuum fluid mechanics accurate when constituents are discrete objects of finite size?

Suppose we view fluids classically, i.e., as a collection of molecules (with some finite size) interacting via e&m and gravitational forces. Presumably we model fluids as continuous objects that ...
4
votes
1answer
151 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 ...
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0answers
145 views

Question on energies obtained via WKB approximation

Suppose we are given an ODE problem $$ y''(x)+V(x)f(x)=E_{n} y(x) $$ with boundary conditions $ y(0)=y(\infty)=0$. Here $V(x)$ is a potential function. Then is it always true that (for $n ...
2
votes
1answer
289 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 ...
8
votes
3answers
716 views

Special Relativistic approximation to GR

Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR ...