Solve Eigenstate of i(d/dx): Find Finite Wave Function

[neelakash]

Homework Statement

I am to find the eigenstate of the operator i(d/dx)

Homework Equations

The Attempt at a Solution

After writing the eigenvalue equation with eigenvalue a, I got

|psi|=exp [(a/i)x+C] where C is the constant of integration...

Now, I do not understand what will be the result, if I omit the || sign from psi

The wave function has to be finite all the way-so,should there be any -ve sign before the exponent?

 

[malawi_glenn]

Can you show how you did it, |psi|=exp [(a/i)x+C] is very wrong in my opinion.

Hint: what function has the same derivate as itself?

Then generalize it.

And by the way, exp(-i*ax+C) is finite for all real x.