1
vote
1answer
93 views

Free particle propagator - Evaluating Integral

In path integral formalism, when evaluating the free particle propagator, we obtain the functional integral of the form, $$ K_0 = \lim_{n\rightarrow\infty} \bigg( \frac{m}{2\pi ...
2
votes
1answer
457 views

Momentum variance in momentum space for particle in a box

My assignment asks me to compute the momentum space wavefunction of the nth energy eigenstate of the particle in a one-dimensional infinite square well, then "show that your result is in agreement ...
1
vote
2answers
158 views

Calculating the expectation value for kinetic energy $\langle E_k \rangle$ for a known wave function

I have a wavefunction ($a=1nm$): $$\psi=Ax\exp\left[\tfrac{-x^2}{2a}\right]$$ for which I already calculated the normalisation factor (in my other topic): $$A = \sqrt{\frac{2}{a\sqrt{\pi a}}} = ...
1
vote
1answer
253 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 ...
3
votes
3answers
378 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?
4
votes
3answers
383 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
139 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, ...