1. One-dimensional point interaction with Griffiths' boundary conditions.
- Author
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Coutinho, F.A.B., Nogami, Y., and Toyama, F.M.
- Subjects
- *
BOUNDARY value problems , *QUANTUM theory , *WAVE functions , *NATURAL numbers , *SELFADJOINT operators , *DERIVATIVES (Mathematics) , *WAVE mechanics , *MATHEMATICAL analysis - Abstract
Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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