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In this chapter, we shall investigate the interaction of
a nonrelativistic particle of mass and energy with various
onedimensional potentials, . Since we are searching for stationary
solutions with unique energies, we can write the wavefunction in the form (see Sect. 4.12)

(300) 
where satisfies the timeindependent Schrödinger equation:

(301) 
In general, the solution, , to the above equation must be
finite, otherwise the probability density would
become infinite (which is unphysical). Likewise, the solution must be
continuous, otherwise the
probability current (155) would become infinite (which is also
unphysical).
Richard Fitzpatrick
20100720