On the Uniform Upper Bounds to the Ground State Energy of Quantum System

Abstract

We derive a set of improving uniform upper bounds to the ground state energy of a quantum system, which provides a natural generalization of the Ritz variational principle. The bounds have a general character, do not depend on the structure of Hamiltonian of a quantum system and converge to its exact ground state energy. As an illustration of the method proposed, we consider a simple example of the shifted harmonic oscillator.