Tagged Questions
1
vote
1answer
147 views
Shift operator (integral calculus involving Hermite polynomials) [closed]
I didn't know whether to pose this question on Physics.stackexchange or Math.stackexchange. But since this is the last step of a development involving the eigenfunctions of an Harmonic oscillator and ...
0
votes
0answers
264 views
Expectation value of a Gaussian wave packet [closed]
How can I compute the expectation value $\langle x\rangle_t$ of a Gaussian wave packet $$\psi(x,t) = \int_{-\infty}^\infty \mathrm dp \, \hat\psi(p) \exp{\frac{-\mathrm i(px - E_p t)}{\hbar}}? $$
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3
votes
3answers
260 views
How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$
What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
3
votes
3answers
308 views
Why we use $L_2$ Space In QM?
I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space ...
13
votes
1answer
109 views
Monte Carlo integration over space of quantum states
I am currently facing the problem of calculating integrals that take the general form
$\int_{R} P(\sigma)d\sigma$
where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
