Analytical solutions of the one-dimensional Schr\"{o}dinger equation with position-dependent mass

• URL: http://arxiv.org/abs/2103.10721v1
• Date: Fri, 19 Mar 2021 10:28:06 GMT
• Title: Analytical solutions of the one-dimensional Schr\"{o}dinger equation with position-dependent mass
• Authors: Tiberiu Harko, Man Kwong Mak
• Abstract summary: The study of the Schr"odinger equation with the position-dependent effective mass has attracted a lot of attention. In the present work we obtain several classes of solutions of the one-dimensional Schr"odinger equation with position-dependent particle mass.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The study of the Schr\"{o}dinger equation with the position-dependent effective mass has attracted a lot of attention, due to its applications in many fields of physics, including the properties of the semiconductors, semiconductor heterostructures, graded alloys, quantum liquids, Helium-3 clusters, quantum wells, wires and dots etc. In the present work we obtain several classes of solutions of the one-dimensional Schr\"{o}dinger equation with position-dependent particle mass. As a first step the single particle Schr\"{o}dinger equation with position-dependent mass is transformed into an equivalent Riccati type equation. By considering some integrability cases of the Riccati equation, seven classes of exact analytical solutions of the Schr\"{o}dinger equation are obtained, with the particle mass function and the external potential satisfying some consistency conditions.

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