Particle in one dimensional potentional well

[derp267]

I hope this is in the right place, I'm new here. Anyway, my teacher hasn't shown us an example where U is anything but infinity, Uo, or 0 and I'm completely stumped on part B for this question since U is a function of x

Homework Statement

A particle of mass m moves in a one-dimensional potential well:
U(x)={infinity...x<0
{-hbar^2/mbx...x>=0

The normalized wave function is:
Ψ (x)={0...x<0
{Axe^(-x/b)...x>=0

Where b and A are constants.
a) Describe in words or equations how you would evaluate A( you do not need to actually evaluate for A).
b) Prove that the above Ψ (x) for x>=0 is an acceptable wave function
c) Find the total energy of the particle. Express your answer in the simplest terms

Homework Equations

The Attempt at a Solution

I did this on paper already and I don't know how to type an integral or anything so I just made a picture..apologies for the bad handwriting
http://imgur.com/OV8RN

So do I make -2mE/hbar^2 -k^2? Then I'm still left with -2/bx and I don't think I can use eulers method with that..I'm stuck

 

[ideasrule]

Assuming you didn't make any algebra errors, your math is correct so far. Since you're trying to prove that Ψ (x) is a solution for x>0, plug their wavefunction into your final equation and see if the left and right sides equal one another. Remember that you can adjust the constant E to try to make the two sides equal, but E is a constant, so it can't depend on x.

 

[derp267]

Thanks for your relpy. Okay so I did as you said and plugged in Axe^(-x/b) for Ψ and did some algebra. Then I did the second derivative of Ψ(x) and set them equal to each other.

What I end up with is the following:
http://i.imgur.com/mflUG.png

So does that mean that E=(-hbar^2)/(2mb^2)?

 

[ideasrule]

Assuming your algebra is right, yes. That's the energy which corresponds to the given wavefunction.