Schroedinger Operator: Heat Kernel and Its Applications

Details Schroedinger Operator: Heat Kernel and Its Applications Schroedinger Operator: Heat Kernel and Its Applications

2011-01-10

arxiv.org/abs/1101.1792v3

Mathematics

Analysis of PDEs

Kernel formulas are recalculated. 24 pages 0 figures

Scientific paper

In this paper, we study the geometry associated with Schroedinger operator via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique, we construct the heat kernel with the coefficient matrices of the operator both diagonal and non-diagonal. For applications, we compute the heat kernel of a Schroedinger operator with terms of lower order, and obtain a globally closed solution to a matrix Riccati equations as a by-product. Besides, we finally recover and generalise several classical results on some celebrated operators.

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