General series solution for finite square-well energy levels for use in wave-packet studies
David L. Aronstein and C. R. Stroud, Jr.
Am. J. Phys. 68, 943 (2000).
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We develop a series solution for the bound-state energy levels of the
quantum-mechanical one-dimensional finite square-well potential. We show
that this general solution is useful for local approximations of the energy
spectrum (which target a particular energy range of the potential well for
high accuracy), for global approximations of the energy spectrum (which
provide analytic expressions of reasonable accuracy for the entire range of
bound states), and for numerical methods. This solution also provides an
analytic description of dynamical phenomena; with it, we compute the time
scales of classical motion, revivals, and super-revivals for wave-packet
states excited in the well.
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