Title: Quantum theory of anharmonic oscillators. I. Energy levels of oscillators with positive quartic anharmonicity
Abstract:This is an investigation of the energy levels of an anharmonic oscillator characterized by the potential (1/2) x2+λx4. Two regions of λ and n are distinguishable (n being the quantum number of the ene...This is an investigation of the energy levels of an anharmonic oscillator characterized by the potential (1/2) x2+λx4. Two regions of λ and n are distinguishable (n being the quantum number of the energy level) one in which the harmonic oscillator levels En=n+1/2 are only slightly distorted and the other in which the purely quartic oscillator form En?cλ1/3(n+1/2)4/3 (c being a constant) is only slightly distorted. Rapidly converging algorithms have been developed, using the Bargmann representation, from which energy levels in any (λ,n) (with λ≳0) regime can easily be computed. Simple formulas are also derived which give excellent approximations to the energy levels in various (λ,n) regimes.Read More
Publication Year: 1975
Publication Date: 1975-09-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 223
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