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Generalized function solution of step potentials
Author(s) -
Ünal Basri
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5174
Subject(s) - mathematics , eigenfunction , operator (biology) , completeness (order theory) , spectrum (functional analysis) , mathematical analysis , transformation (genetics) , square (algebra) , function (biology) , symmetry (geometry) , pure mathematics , eigenvalues and eigenvectors , quantum mechanics , evolutionary biology , biology , biochemistry , physics , chemistry , geometry , repressor , transcription factor , gene
Schrödinger equation is solved for step function–like potentials within the class of generalized functions. The solution functions carry the same symmetry as the potential. It is shown that the ground state energy is always equal to the minimum value of the potential. Finite square well potential has eigenfunctions both for continuous and discrete spectrum, they form a complete set, and the discrete spectrum does not depend on the well depth. A theorem on the completeness property of transformation operator is proved.