H2: entanglement, probability density function, confined Kratzer oscillator, universal potential and (Mexican hat- or bell-type) potential energy curves

TL;DR

This paper reviews harmonic oscillator theory for quantum systems, demonstrating that a confined Kratzer oscillator provides superior potential energy curves for H2 molecules, simplifies chemical bonding theory, and quantifies entanglement and probability distributions.

Contribution

It introduces a confined Kratzer oscillator approach that yields a universal potential energy function, improving upon traditional methods and applicable across molecular and nuclear scales.

Findings

Confined Kratzer oscillator produces better H2 PECs than RKR.

Quantifies entanglement of H2 quantum states.

Validates universal potential with multiple molecules.

Abstract

We review harmonic oscillator theory for closed, stable quantum systems. The H2 potential energy curve (PEC) of Mexican hat-type, calculated with a confined Kratzer oscillator, is better than the Rydberg-Klein-Rees (RKR) H2 PEC. Compared with QM, the theory of chemical bonding is simplified, since a confined Kratzer oscillator gives the long sought for universal function, once called the Holy Grail of Molecular Spectroscopy. This is validated with HF, I2, N2 and O2 PECs. We quantify the entanglement of spatially separated H2 quantum states, which gives a braid view. The equal probability for H2, originating either from HA+HB or HB+HA, is quantified with a Gauss probability density function. At the Bohr scale, confined harmonic oscillators behave properly at all extremes of bound two-nucleon quantum systems and are likely to be useful also at the nuclear scale.