- #1

jg370

- 18

- 0

## Homework Statement

jg370 said:Hi,

My question relates to the solution to a question regarding the expectation value of momentum, that is [tex]<p^2>[/tex].

As the solution unfold, we have the following two expressions:

[tex]-\frac{m*\omega*\hbar}{\sqrt Pi}\left[\int_{-\infty}^{\infty} \xi^2 *e^-\xi^2 d\xi-\int_{-\infty}^{\infty} e^-\xi^2 d\xi\right][/tex]

[tex]-\frac{m*\omega*\hbar}{\sqrt Pi}\left[\Gamma(\frac{3}{2}) -\sqrt Pi\right][/tex]

## Homework Equations

My problem with the above, is that I do not understand how one gets from

[tex] \left[\int_{-\infty}^{\infty} \xi^2 *e^-\xi^2 d\xi\right][/tex]

to

[tex]\left[\Gamma(\frac{3}{2}) \right][/tex]

## The Attempt at a Solution

I have reviewed the [tex]\Gamma function[/tex] and tried to make a conversion from the exponential function to the gamma function; this did not lead me to understand the relation ship involved in this case.

I hope that some one can help me with this.

I thank you for your kind assistance

jg370