Kinetic and electrostatic energies in quantum mechanics

TL;DR

This paper examines the nature of kinetic and electrostatic energies in quantum mechanics, emphasizing the importance of excluding self-energies to accurately determine bound state energies and clarifying the energy contributions in quantum systems.

Contribution

It introduces a method to explicitly account for all energy terms in quantum systems, demonstrating the necessity of excluding self-energies for correct energy calculations.

Findings

Correct ground state energy of hydrogen achieved without self-energies.

Electrostatic energy of a neutral charge distribution can be negative.

Self-action should be excluded in quantum energy calculations.

Abstract

A concept of kinetic energy in quantum mechanics is analyzed. Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be understood, using expansion of the wave function into Fourier integral, that is, on the basis of virtual plane waves. The ground state energy of a hydrogen atom is calculated in a special way, regarding explicitly all the terms of electrostatic and kinetic energies. The correct values of the ground state energy and the radius of decay are achieved only when the electrostatic energies of the electron and the proton (self-energies) are not taken into account. This proves again that self-action should be excluded in quantum mechanics. A model of a spherical ball with uniformly distributed charge of particles is considered. It is shown that for a neutral ball (with compensated electric charge) the electrostatic energy is a non-zero negative value in this model. This occurs because the self-energy of the constituting particles should be subtracted. So it shown that the energy of the electric field does not have to be of a positive value in any imaginable problem.