Transition matrix of point interactions as the scaling limit of integrable potentials on the real line. (English) Zbl 0574.46060
On the real line, the non-relativistic one-particle Hamilton operator for a finite number of zero-range interaction points is the scaling limit of the Schrödinger operator for integrable potentials, in the sense of norm-resolent convergence; correspondingly, the transition matrix for such point interaction can be obtained as scaling limit from integrable potentials.
MSC:
| 46N99 | Miscellaneous applications of functional analysis |
| 47F05 | General theory of partial differential operators |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 35J10 | Schrödinger operator, Schrödinger equation |
Keywords:
non-relativistic one-particle Hamilton operator for a finite number of zero-range interaction points; scaling limit of the Schrödinger operator for integrable potentials; norm-resolent convergence; transition matrixReferences:
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