# 1-D infin. potent. well

1. Oct 30, 2009

### Panic Attack

1. The problem statement, all variables and given/known data
I didn't put this in the right format the first time. My question is, I have a 1-D box confined at at x = 0 and x = L. So, points between 0 and L distances are the continuum state and otherwise distances be discontinous.
a) I need to find the egien functs: Un(x) and related egien values: En .... n are the excited levels represented as postive whole numbers.

The wave funct is: φ(x, t = 0) = (1/(3^1/2))U_2(x) + ((2/3)^1/2)U_3(x)

b) As time progresses, what will the function look like?
c) What is the prob. density (φ squared) and P(x,t) = total probability.

2. Relevant equations
Schrodinger Eq.

3. The attempt at a solution

What I have so far...

(-(h/2pi)^2)/2m * (d^2/dx^2)Psi(x) = E*Psi(x)
Psi(x)|x=0 = Asin(0) + Bcos(0) = B = 0 ?
Psi(x)|x=L = Asin(kL) + Bcos(kL) = 0 ?

[0 0; sin(kL) cos(kL)] *[A;B] = [0 0]

set KnL/2 = n*pi
En = (h/2pi)^2 *k^2]/2m
= [(h/2pi)^2] /2m * (2n*pi/L)