• Support PF! Buy your school textbooks, materials and every day products Here!

Finding psi(x,t) using psi(x)

  • Thread starter JordanGo
  • Start date
  • #1
73
0

Homework Statement


Consider the free-particle wavefunction,
ψ(x)=(pi/a)^(-1/4)*exp(-ax^2/2)

Find ψ(x,t)


The Attempt at a Solution



The wavefunction is already normalized, so the next thing to find is coefficient expansion function (θ(k)), where:

θ(k)=∫dx*ψ(x)*exp(-ikx) from -infinity to infinity

But this equation seems to be impossible to solve without error function (as maple 16 tells me).

Is there any trick to solve this?
 

Answers and Replies

  • #2
6,054
390
The error function has very nice properties at the infinity, so you should be able to compute the integral. Alternatively, you could use the apparatus of complex analysis to evaluate the integral.
 
  • #3
52
0
Why not use some of the simple Gaussian integral tricks (like completing the square in the exponential)? Or am I missing something?
 
  • #4
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,538
1,150
You can avoid the error function because of the limits on the integral, or equivalently, use the nice properties of the error function at those limits.

You should really learn to crank this integral out by hand, though. The techniques used are useful to know.
 

Related Threads for: Finding psi(x,t) using psi(x)

  • Last Post
Replies
3
Views
3K
Replies
1
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
9
Views
4K
  • Last Post
Replies
2
Views
8K
Top