REFERENCES
1.
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The trouble was first encountered by people attempting to solve the one-dimensional Dirac equation with a single delta-function potential (“one-dimensional hydrogen”) or with an array of delta functions (“relativistic Kronig–Penney model”). Allowed energies and scattering amplitudes derived using (2) do not agree with those obtained from the appropriate limit of rectangular potentials. Incidentally, the same difficulty arises for the Schrödinger equation with a potential proportional to the derivative of a delta function.
4.
There may be other ways to interpret Eq. (3), but this much is certainly true: naive application of Eq. (2) is likely to lead to serious inconsistencies.
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© 1999 American Association of Physics Teachers.
1999
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