Generalized Gelfand-Yaglom Formula for a Discretized Quantum Mechanic System
Mathematical Physics
2021-12-08 v4 math.MP
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.
Cite
@article{arxiv.2011.02996,
title = {Generalized Gelfand-Yaglom Formula for a Discretized Quantum Mechanic System},
author = {Meredith Shea},
journal= {arXiv preprint arXiv:2011.02996},
year = {2021}
}
Comments
18 pages