A simple eigenvalue formula for the quartic anharmonic oscillator
The eigenvalues Enl(λ) of the Hamiltonian H = −Δ + r2 + λr4 are analysed with the help of "potential envelopes" and "kinetic potentials." The result is the following simple approximate eigenvalue formiula:[Formula: see text]where E ≥ P = (4n + 2l − 1) and Q = 3(An + Bl − C)4/322/3. E is a lower bound to Enl if (A, B, C) = (1, 1/2, 1/4) and a good approximation if (A, B, C) = (1.125, 0.509, 0.218).
Keyword(s):
2011 ◽
Vol 33
(3)
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pp. 701-705
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Keyword(s):
1989 ◽