What is the Ground State Wave Function for an Electron in a 1D Potential?

[ktravelet]

Homework Statement

an electron moves in 1D and is confined to the right half (x>0)
potential: V(x) = -(e^2)/(8piEx) E is the permittivity of free space
the ground state wave function is Nxe^(-ax)
N is normalization constant, and a is another constant needed to be determined

Homework Equations

time independent Schrödinger: (-h^2/2m) (d^2Si/dx^2) + V*Si = E*Si

The Attempt at a Solution

The first part of this problem tells my to substitute the ground state wave function in the appropriate TISE to determine a.

I am completely lost on this one because I usually substitute V(x) into the TISE to determine a and I never had to do it the way they are describing. I tried to sub the wave function into the standard TISE and got:

(ax+2)/a^2 = (E-V)(-2xm)/(h^2) - this is after doing the double derivative of the wave function etc.

However I still can't solver for just a doing the way I tried.
Please help, thanks.

 

[CompuChip]

I am completely lost on this one because I usually substitute V(x) into the TISE

Why can't you do that here? V(x) is given, it is V(x) = -(e^2)/(8piEx) according to you. Also, psi is given. If you plug it in you will get an equation containing a's. So it will tell you what a can be such that the given ground state wavefunction is indeed a solution of the TISE for the given potential.