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The quantum mechanical version of this harmonic oscillator problem may
be written as
By considering the limiting behavior as
and
as
, one finds that only certain energies
yield
reasonable solutions
. The eigenvalues and associated
eigenvectors are
where
are the Hermite polynomials of order
. The Hermite
polynomials have a number of useful properties such as
Subsections
Next: Units
Up: ho
Previous: Classical Harmonic Oscillator
David Sherrill
2002-10-16