CRC Press eBooks

Schrödinger Equation for Central Potentials and 3D System

Aditi Sharma

Published Jun 18, 2021• 0 citations

Abstract

Solutions of the Schrödinger equation for central potentials and for cubic systems are the main contents of the chapter. Motion in a central field, energy eigenvalues and wave functions for the hydrogen atom, radial probability density, solutions for the 3D spherically symmetric potential well, and free electron motion in a 3D-box are discussed with the use of algebra that clarifies the essential physics in a simple but appealing manner. Derivation of energy eigenvalues for the hydrogen atom and for a free electron cubic box clearly illustrates the concept of quantization of energy. The number of states and the density of states are introduced for the case of an electron confined to a cubic box. Carefully chosen solved examples further consolidate the understanding of solutions of the Schrödinger equation for central potentials and for a cubic system.

DOI: 10.1201/9781003154457-6

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