(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle with energy greater than the potential is defined as below:

V(x) = Vo (x<0)

V(x) = 0 (0<x<a)

V(x) = Vo (x>a)

a) Write the complete solutions (time and space) to the S. Eqn for the 3 regions

b) What condition must the width of the potential satisfy for the transmission of a wave from the left to be a maximum?

c) What is the minimum possible value for the transmission? What conditions must the weidth of the potential satisfy for this?

2. Relevant equations

None, really. It seems more conceptual.

3. The attempt at a solution

If I am not mistaken, this represents a simple harmonic oscillator.

I believe to have figured out the answer to part A.

Region 2 has the Schrodinger equation:

(-h(bar)/2m)(d^{2}[tex]\psi[/tex]/dx^{2}) + 1/2kx^{2}[tex]\psi[/tex] = ih(bar)d[tex]\psi[/tex]/dt

whose bound state solutions are [tex]\psi[/tex](x,t)=[tex]\psi[/tex](x)e^(-iEt/h(bar))

The solution for Region 1 = Region 3 is:

(-h(bar)/2m)(d^{2}[tex]\psi[/tex]/dx^{2}) + 1/2kx^{2}[tex]\psi[/tex] = ih(bar)d[tex]\psi[/tex]/dt

[tex]\psi[/tex]''(x)=(alpha)^{2}[tex]\psi[/tex](x) where (alpha)^{2}= (2m/h(bar)^{2})(V(x)-E)

For problem b, I have an idea that since the wave function is Asinkx, the length (x) would have to be long enough so that it reaches a maximum at the second barrier (sin(pi/2)).

I could be going about this problem completely wrong. I've read through the textbook many times and it just doesnt reach this level of detail.

Any help would be much appreciated!!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Particle in finite well (Schroedinger)

**Physics Forums | Science Articles, Homework Help, Discussion**