Study on quantum mechanical propagators and path integrals

点击翻译按钮获取中文摘要

This research concerns the quantum-mechanical propagator, namely, the integral kernel of the Schrodinger unitary group, Green function as well as their imaginary-time version, the integral kernel of the Schrodinger semi-group and heat kernel. Results are obatined among others on the following two topics. One is to investigate how good an approximation is given to the integral kernel of the Schrodinger semi-group or heat kernel by path integral based on the operator-norm selfadjoint Trotter product formulas obtained, and the other is to revisit with some new aspects the problem on the imaginary-time path integral representation for three relativistic Schrodinger operators.