Potential Well Problem: Finding Excited States and Wave Functions

[noblegas]

Homework Statement

A particle of mass m moves in one dimension in the following potential well:

V(x)=infinity, x<0 , x>L/3
V(x)=0 , 0<x<L/3

a)Circle the general functional form of the 1st excited wave function phi_1(x) in the region 0<x<L/3. k is a positive constant; A is constant as well;

i) A sin(kx)
ii) A cos(kx)
iii) A exp(kx)
iv) A exp(-kx)

b) use the boundaries conditions to determine k
c)Find A
d)Find the 2nd excited state)

Homework Equations

The Attempt at a Solution

a) I figured out was iv)
b) Not sure what to do here but I will give it a try; A*exp(-k*L/3)-A*exp(-k*0)=0 and A*exp(k*infinty)-A*exp(-k*infinity)=infinity)
c) I would squared phi to get A; (A*exp(-kx))^2=0, x=0...L/3

d) E=n*h*omega, where n=2?

 

[George Jones]

a) I figured out was iv)

How did you find this?

 

[noblegas]

How did you find this?

For some reason I assumed that L/3 was approaching infinity;
I think phi =A*sin(kx) since sin(k*x=0)=0 and sin(k*L/3)= 0, assuming L is the value of a unit; This implies k=3pi,9pi,15pi,...

to find A, I would normilized phi, i.e., A^2*sin^2(3pi*x)=1, not sure what x would be

E=n*h*omega, n=2

 

[noblegas]

Was the second approach I applied wrong as well?