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Consider a particle constrained to move in a single dimension, under
the influence of a potential which is zero for
and
infinite elsewhere. Since the wavefunction is not allowed to become
infinite, it must have a value of zero where is infinite, so
is nonzero only within . The Schrödinger equation
is thus

(115) 
It is easy to show that
the eigenvectors and eigenvalues of this problem are

(116) 

(117) 
Extending the problem to three dimensions is rather straightforward;
see McQuarrie [1], section 6.1.
David Sherrill
20060815