- #1

javaman1989

- 6

- 1

## Homework Statement

I'm working on problem 2.22 from Griffith's Intro. to Quantum Mechanics (a free particle problem). I am stuck on the final integral from part b. Part a of the problem is normalizing:

A*e

^{-a*x2}which I did. Part b wants the general, time-dependent wave function.

## Homework Equations

Griffith says that integrals of the form

∫e

^{-(a*x2+b*x)}can be solved by "completing the square." Griffith gives the example of defining y to be (a)

^{(1/2)}*(x+(b/(2a)) and using that definition to convert (a*x

^{2}+b*x) to y

^{2}- (b

^{2}/(4*a)) I presume we are supposed to substitute in the converted expression into the integral and work from there.

## The Attempt at a Solution

I have the following integral:

∫e

^{-k2/(4*a)+i*(k*x-(h*k2)/(2*m)*t)}

I presume using the "completing the square" method is supposed to make this integral work out; but I don't see how this will help. If I do convert this into something like:

e

^{y + (something about a, h, and m)},

how do I integrate with y?

Thanks,

Vance