Morse potential derived from first principles

¹ Departamento de Física, Universidade Federal do Ceará - Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil
² Faculdade de Educação, Ciências e Letras do Sertão Central, Universidade Estadual do Ceará R. Epitácio Pessoa, 2554, 63.900-000 Quixadá, Ceará, Brazil
³ Department of Physics, The Norwegian University of Science and Technology - N-7491 Trondheim, Norway
⁴ Centre for Advanced Study (CAS) - Drammensveien 78, N-0271 Oslo, Norway

^(a) rai@fisica.ufc.br
^(b) geova@fisica.ufc.br
^(c) bo-sture.skagerstam@ntnu.no
^(d) soares@fisica.ufc.br

Received: 15 October 2012
Accepted: 21 December 2012

Abstract

We show that a direct connection can be drawn, based on fundamental quantum principles, between the Morse potential, extensively used as an empirical description for the atomic interaction in diatomic molecules, and the harmonic potential. This is conceptually achieved here through a non-additive translation operator, whose action leads to a perfect equivalence between the quantum harmonic oscillator in deformed space and the quantum Morse oscillator in regular space. In this way, our theoretical approach provides a distinctive first-principle rationale for anharmonicity, therefore revealing a possible quantum origin for several related properties as, for example, the dissociation energy of diatomic molecules and the deformation of cubic metals.