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Analytical Solutions of the Schrödinger Equation with Power Potentials
Author(s) -
Karwowski Jacek,
Witek Henryk A.
Publication year - 2016
Publication title -
journal of the chinese chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 45
eISSN - 2192-6549
pISSN - 0009-4536
DOI - 10.1002/jccs.201400540
Subject(s) - chemistry , polynomial , integer (computer science) , schrödinger equation , power (physics) , mathematical physics , thermodynamics , mathematical analysis , physics , mathematics , computer science , programming language
Conditions for the existence of polynomial solutions of the Schrödinger equation with potentials which are linear combinations of powers of r ranging from −2 to 2 m , where m is a non‐negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.