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A Second Order Differential Operator with Eigenvalue Degeneracy
Author(s) -
Hochstadt Harry
Publication year - 1972
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm197251199
Subject(s) - eigenvalues and eigenvectors , differential operator , degeneracy (biology) , mathematics , degenerate energy levels , operator (biology) , order (exchange) , mathematical analysis , mathematical physics , pure mathematics , physics , quantum mechanics , chemistry , bioinformatics , biochemistry , finance , repressor , gene , transcription factor , economics , biology
The second order differential operator Lu = − u ″ + ( M − |x|) u defined on ( −∞, ∞) is analyzed. It is shown that the pair of successive eigenvalues λ 2 n , λ 2 n +1 is asymptotically degenerate as M becomes large, for all n .
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