Schrodinger's Equation in Riemann Spaces

TL;DR

This paper explores properties of Beltrami differential operators in metric spaces and solves Schrödinger's equation for various potentials, analyzing the self-adjointness of the Hamiltonian in different spaces.

Contribution

It introduces new insights into Beltrami operators in metric spaces and extends solutions of Schrödinger's equation to a broader class of spaces.

Findings

Properties of Beltrami operators in metric spaces

Solutions of Schrödinger's equation for various potentials

Conditions for Hamiltonian self-adjointness

Abstract

We present some properties of the first and second order Beltrami differential operators in metric spaces. We also solve the Schroedinger's equation for a wide class of potentials and describe spaces that the Hamiltonian of a system physical is self adjoint.