Energy-dependent point interaction: Self-adjointness

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Data

2006-11-01

Autores

Coutinho, F. A. B.
Nogami, Y.
Tomio, Lauro
Toyama, F. M.

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Natl Research Council Canada-n R C Research Press

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Recently, we constructed an energy-dependent point interaction (EDPI) in its most general form in one-dimensional quantum mechanics. In this paper, we show that stationary solutions of the Schrodinger equation with the EDPI form a complete set. Then any nonstationary solution of the time-dependent Schrodinger equation can be expressed as a linear combination of stationary solutions. This, however, does not necessarily mean that the EDPI is self-adjoint and the time-development of the nonstationary state is unitary. The EDPI is self-adjoint provided that the stationary solutions are all orthogonal to one another. We illustrate situations in which this orthogonality condition is not satisfied.

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Canadian Journal of Physics. Ottawa: Natl Research Council Canada-n R C Research Press, v. 84, n. 11, p. 991-1005, 2006.