The Strong Convergence of Schrodinger Propagators
Copyright policy )The Strong Convergence of Schrodinger Propagators
Time dependent versions of the Trotter-Kato theorem are discussed using nonstandard analysis. Both standard and nonstandard results are obtained. In particular, it is shown that if a sequence of generators converges in the strong resolvent topology at each time to a limiting generator and if the sequence of generators and limiting generator uniformly satisfy Kisynski type hypotheses then the corresponding Schrodinger propagators converge strongly. The results are used to analyze time dependent, form bounded perturbations of the Laplacian.
Linear symmetric and selfadjoint operators (unbounded), Groups and semigroups of linear operators, Schrödinger operator, Schrödinger equation, Perturbations in context of PDEs, positive selfadjoint operator, strong convergence of Schrödinger propagators, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Trotter-Kato theorem, nonstandard analysis
Linear symmetric and selfadjoint operators (unbounded), Groups and semigroups of linear operators, Schrödinger operator, Schrödinger equation, Perturbations in context of PDEs, positive selfadjoint operator, strong convergence of Schrödinger propagators, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Trotter-Kato theorem, nonstandard analysis
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