Journal of Applied Mathematics and Physics, 2021, 9, 306-316 https://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352 DOI: 10.4236/jamp.2021.92022 Feb. 25, 2021 306 Journal of Applied Mathematics and Physics A Model Effective Mass Quantum Anharmonic Oscillator and Its Thermodynamic Characterization M. Vubangsi 1,2* , F. B. Migueu 2 , B. F. Kamsu 2 , L. S. Yonya Tchapda 2 , M. Tchoffo 2,3 , L. C. Fai 2 1 Computational Material Science Lab, Department of Computer Science, HTTTC Bambili, University of Bamenda, Bambili, Cameroon 2 Unité de Recherche de Matière Condensée, d’Électronique et de Traitement du Signal, Département de Physique, Faculté des Sciences, Université de Dschang, Dschang, Cameroon 3 Centre d’Études et de Recherches en Agronomie et en Biodiversité, FASA, Université de Dschang, Cameroon Abstract Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic os- cillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges. Keywords Ordering Ambiguity, Anharmonicity Parameter, Variable Mass, Anharmonic Oscillator, Thermodynamic Resonance, Complex Entropy, Quantum Harmonic Oscillator 1. Introduction In material science, the electron effective mass * m is the mass, it appears to have when probed in the periodic potential of a crystal lattice. The quantum mechanical description of this phenomenon is furnished by the effective mass approximation which is the Schrödinger equation given by: How to cite this paper: Vubangsi, M., Mi- gueu, F.B., Kamsu, B.F., L.S.Y., Tchapda, Tchoffo, M. and Fai, L.C. (2021) A Model Effective Mass Quantum Anharmonic Os- cillator and Its Thermodynamic Characteri- zation. Journal of Applied Mathematics and Physics, 9, 306-316. https://doi.org/10.4236/jamp.2021.92022 Received: January 26, 2021 Accepted: February 22, 2021 Published: February 25, 2021 Copyright © 2021 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access