Quantum SHM with Finite Potential and Hermite Polynomials

[Larry89]

Let it be V=(1/2)m(w^2)(x^2) for -L<x<L and V=A finite for x elsewhere.

is it obvious to use the wavefunction for the SHO that has infinite limits for the (-L,L) region and the usual decay of tunneling for the parts outside x</L/, and then play with the boundary conditions to determine the constants?

thanks for any discussion.

PS: I am particularly interested in the case that the particle energy is less than A but any further ideas are more than welcomed.

 

[weejee]

You should use Hermite polynomials (H_n) with arbitrary non-integer n's