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The Schrödinger equation with a moving point interaction in three dimensions
Author(s):
Andrea
Posilicano
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1785-1793.
MSC (2000):
Primary 47B25, 47D08;
Secondary 47D06, 81Q10
Posted:
December 27, 2006
MathSciNet review:
2286089
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Abstract:
In the case of a single point interaction we improve, by using different methods, the existence theorem for the unitary evolution generated by a Schrödinger operator with moving point interactions obtained by Dell'Antonio, Figari and Teta.
References:
-
- 1.
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- 2.
- Dell'Antonio, G.F., Figari, R., Teta, A.: The Schrödinger equation with moving point interactions in three dimensions. Stochastic processes, physics and geometry: new interplays, I (Leipzig, 1999), 99-113, CMS Conf. Proc. 28, Amer. Math. Soc., Providence, RI, 2000 MR 1803381 (2002g:81028)
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 n-like formula for singular perturbations of self-adjoint operators and applications. J. Funct. Anal. 183 (2001), 109-147 MR 1837534 (2002m:47018) - 8.
- Simon, B.: Quantum Mechanics for Hamiltonians Defined as Quadratic Forms. Princeton University Press, Princeton, N. J., 1971 MR 0455975 (56:14207)
- 9.
- Teta, A.: Quadratic forms for singular perturbations of the Laplacian. Publ. RIMS, Kyoto Univ. 26 (1990), 803-817 MR 1082317 (92g:35027)
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MSC (2000):
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MSC (2000):
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47D06, 81Q10
Additional Information:
Andrea
Posilicano
Affiliation:
Dipartimento di Fisica e Matematica, Università dell'Insubria, I-22100 Como, Italy
Email:
posilicano@uninsubria.it
DOI:
10.1090/S0002-9939-06-08814-9
PII:
S 0002-9939(06)08814-9
Keywords:
Point interactions,
singular perturbations,
unitary propagators.
Received by editor(s):
February 3, 2006
Posted:
December 27, 2006
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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