[love48]

*The wave function Ψ(theta), for the motion of a particle in a ring is  Ψ= Ne^(imφ).
Determine the normalization constant.

*a)  Find the values of the constant "a" that makes exp(-ax^2) an eigenfucntion oof the operator d^2/dx^2 - bx^2 where B is constant. What is corresponding eigenvalue?
   b) show that the function f(x) = x exp (-ax^2) is an eigenfunction of the operator in part a) if the constant "a" is properly chosen, find its eigenvalue:
these function are basic to the quantum mechanical theory of vibrating systems.

[love48]

for the first one, i never learned normalization factor and i don't get what the second question for eigenfunction is trying to ask. I know how to to do eigenfunction and find its value but i don't what this one is asking for.

[tamim83]

A "normalized" function satisfies,



You need to integrate over all space (from to ) or within the boundary conditions for the problem.  I think for this though you need to use the boundary conditions for particle on a ring.  

So, to normalize the function, you need to find a value of N that satisfies the normalization condition.  

Note: To get the complex conjugate ( ), replace all "i' with "-i".  

[love48]

I can't see the image you posted. I use Google Chrome

[tamim83]

I can't see the image you posted. I use Google Chrome

Ok.  The normalization condition is that the integral over all space for the wavefunction multiplied by its complex conjugate is equal to one.  Like I said, since your problem has boundary conditions, you need to integrate over those instead of "all space".  Does that help some?  

[love48]

yes got the answer :-)
N = 1/ Squre root of 2pie

do you know the other one?

[love48]

Thank you