1
vote
1answer
171 views

Integrals involving Hermite Polynomials

Could you please tell me, How to evaluate this integral which involve hermite polynomials, $\int_{-\infty}^\infty e^{-ax^2}x^{2q}H_m(x)H_n(x)\,dx=?$ where $H_n$ is the $n$-th Hermite polynomial ...
1
vote
1answer
131 views

Evaluate an Integral involving Gaussian divided by square root of a quartic polynomial

Could you please tell me, How to evaluate the integral, $\int_{-\infty}^\infty\int_{-\infty}^\infty\dfrac{e^{-a(x^2+y^2)}}{\sqrt{k^2+\beta^2(x^2-y^2)^2}}dx~dy$ I already have obtained a series ...
1
vote
1answer
42 views

Unwanted $i$ floating around when trying to calculate $\langle p\rangle$

$\def\sp#1{\left\langle#1\right\rangle}$I am given $$ \Psi(x,0)=A_0 \exp\left(-\frac{x^2}{2\sigma_0^2}\right) \cdot \exp\left(\frac{i}{\hbar}p_0x\right)\tag1$$ where $A_0=(\pi ...
2
votes
0answers
128 views

How do I solve this integral

How do I solve this integral (expectation value) : $$\int_{-\infty}^{\infty} \psi (x)^* \hat p \psi (x)\ dx.$$ where the $\hat p =-i\hbar \frac {\partial}{\partial x}$ is an operator and $\psi (x)$ is ...
0
votes
1answer
343 views

triple integral (quantum mechanics)

I recently started a quantum mechanics course after a long time with no serious maths and I'm having some problems with the most basic maths operations. Please, help me solve this triple integral ...