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- Energy-dependent point interaction: Self-adjointness
- McMaster Univ
- Universidade de São Paulo (USP)
- Universidade Estadual Paulista (UNESP)
- Kyoto Sangyo Univ
- 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.
- Canadian Journal of Physics. Ottawa: Natl Research Council Canada-n R C Research Press, v. 84, n. 11, p. 991-1005, 2006.
- Natl Research Council Canada-n R C Research Press
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