Generalized Gelfand-Yaglom Formula for a Discretized Quantum Mechanic System
arXiv:2011.02996 · doi:10.1063/5.0059030
Abstract
The Gelfand-Yaglom formula relates the regularized determinant of a differential operator to the solution of an initial value problem. Here we develop a generalized Gelfand-Yaglom formula for a Hamiltonian system with Lagrangian boundary conditions in the discrete and continuous settings. Later we analyze the convergence of the discretized Hamilton-Jacobi operator and propose a lattice regularization for the determinant.
18 pages