# Integration seems gaussian but the answer does not match

1. Nov 30, 2014

### tfhub

1. The problem statement, all variables and given/known data

-h^2/2m (sqrt(2b/pi)) e^(-bx^2) d^2/dx^2 (e^(-bx^2)) dx from - to + infinity

2. Relevant equations
I tried differentiating e^(-bx^2) twice and it came up weird , I positioned the values and finally cam up with (-2b sqrt(pi/2b)........is there any other way to do it ?

3. The attempt at a solution
I tried with gaussian integration and my final answer is h^2b/m but it should be h^2b/2m... how am i missing the 1/2 factor?

2. Nov 30, 2014

### Orodruin

Staff Emeritus
It is difficult to say where you are going wrong if you do not show us exactly what you did step by step.

3. Nov 30, 2014

### Ray Vickson

If you mean that you came up with -2b sqrt(pi/2b) for the integral--that is, that
$$\int_{-\infty}^{\infty} e^{-bx^2} \frac{d^2}{dx^2} e^{-b x^2} \, dx =- 2b \sqrt{\frac{\pi}{2b}},$$
then you are off by a factor or 2: you should have $-b \sqrt{\pi/2b}$. You need to show your work in detail.