A subclass of anharmonic oscillators whose eigenfunctions have no recurrence relations
Author:
Gary G. Gundersen
Journal:
Proc. Amer. Math. Soc. 58 (1976), 109-113
MSC:
Primary 34B25
DOI:
https://doi.org/10.1090/S0002-9939-1976-0460781-4
MathSciNet review:
0460781
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Abstract | References | Similar Articles | Additional Information
Abstract: The equation with a fixed
, possesses a set of solutions
(with associated
) which form a complete orthonormal set for
(as a real space). Here it is shown that any
(fixed
a polynomial with
when
) cannot be expressed as a finite linear combination of
when
is a multiple of 4. It is well known that
can always be expressed as such when
(the Hermite case).
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1976-0460781-4
Keywords:
Eigenfunction,
eigenvalue,
Hermite functions,
Hermite polynomials,
recurrence relation,
complete orthonormal set,
anharmonic oscillator,
harmonic oscillator,
nilpotent Lie algebra,
WKB transformation
Article copyright:
© Copyright 1976
American Mathematical Society