Quantum physics and quantum information April 26, 2016
On a new relation between solutions of the heat equation and Schrodinger equation I. D. Remizov abc a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics b Lobachevski State University of Nizhni Novgorod c Bauman Moscow State Technical University
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Abstract:
We consider a formula derived in 2014, which allows one to express the semigroup with generator -iH through the semigroup with generator -H, where H is a selfadjoint operator in the right-hand side of heat equation and Schrodinger equation. Such a formula is proven within the framework of semigroups and, therefore, is applicable for a wide class of operators and configuration spaces.
Supplementary materials:
remizov_qpqi_26_04_2016.pdf (791.4 Kb)
References
Ivan D. Remizov, Quasi-Feynman formulas – a method of obtaining the evolution operator for the Schrödinger equation original, Journal of Functional Analysis 270 (2016), pp. 4540-4557, DOI information: 10.1016/j.jfa.2015.11.017 , free available preprint http://arxiv.org/abs/1409.8345
I. D. Remizov, Kvazifeinmanovskie formuly dlya gruppy Shredingera: chto eto, kak ikh poluchat, kakaya ot nikh polza, Mezhdunarodnaya konferentsiya po funktsionalnym prostranstvam i teorii priblizheniya funktsii, posvyaschennaya 110-letiyu so dnya rozhdeniya akademika S. M. Nikolskogo
D.V.Grishin, A.V.Smirnov, Quasi-Feynman formulas for the one-dimensional Schrödinger equation with a bounded smoothpotential via the Remizov theorem, International Conference “Infinite-dimensional dynamics,dissipative systems, and attractors” July 13-17, 2015, Nizhny Novgorod
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