1D Quantum Mechanics

  • Thread starter loobloke
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Homework Statement


Given a square well,
Infinite wall at x=0
Wall height U for x>L

For E<U, find solutions to the schrondinger equation inside the well, and beyond x>L which satisy boundary conditions for x=0 and x=[tex]\infty[/tex]

Taking conditions at x=L, find the allowable energies of the system.


Homework Equations


Schrondinger equation


The Attempt at a Solution


Know U=0 inside the well, 0<x<L.

Conditions we get are, (I cant find the wavefunction symbol, Y looks the closest.)
x is continuous at 0, hence Y(0)=0

What condition do I need at x=L? Or am I completely missing the plot.

Do I need to do another condition at x=[tex]\infty[/tex]?
Ie, there are two solutions? One inside the well and one outside?
 

Answers and Replies

  • #2
vela
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Yes, there are two solutions. You need to solve the SE in both regions and then join the solutions smoothly at x=L, i.e., ψ(L-)=ψ(L+) and ψ'(L-)=ψ'(L+).
 

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