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The eigenvalues and eigenfunctions of a spherically symmetric anharmonic oscillator
Author(s) -
Isaacson David,
Marchesin Dan
Publication year - 1978
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160310603
Subject(s) - eigenfunction , mathematics , eigenvalues and eigenvectors , image (mathematics) , spin weighted spherical harmonics , laguerre polynomials , operator (biology) , spherical harmonics , mathematical analysis , anharmonicity , pure mathematics , harmonics , physics , quantum mechanics , computer vision , biochemistry , chemistry , repressor , voltage , computer science , transcription factor , gene
We show that the operator H s has a complete set of eigenfunctionsand eigenvalues, which satisfy[2 l ( l + 1) ‐ (3 n 2 + 3 n + 1)] s + o ( s ) and lim s→0= 0. The functionsare given in spherical coordinates as a product of generalized Laguerre functions and spherical harmonics.