Post on 21-Dec-2015
Boundary conditions for the infinite square well:
These slides make the case for the boundary conditions for the infinite square well by taking the limit of large well depths for the finite square well.
The finite square well wavefunctions were computed using an application found at
http://webphysics.davidson.edu/faculty/dmb/SingleWells/Well2.html
Boundary conditions for infinite barrier:
continuous
can be discontinuous at the barrier edge
under the barrier
x
0
Note that the y axis only shows units of energy. No units are show for the wavefunction, which is ok since all that matters is that the probability is normalized to unity.
Boundary conditions for infinite barrier:
continuous
can be discontinuous at the barrier edge
under the barrier
x
0
Boundary conditions for infinite barrier:
continuous
can be discontinuous at the barrier edge
under the barrier
x
0
Additional discussion about normalizability
Key point: There exist “energy eigenstates” for the finite square well with continuous values of the eigenvalue E. These states are only excluded by the requirement that the wavefunction be normalizable.