Square-Well Approximation for the Anharmonic and the Double-Well Oscillators

2014/05/09 by B. P. Mahapatra, Mahapatra, B. P., N. B. Pradhan +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.1405.2774

openalex publication_date 2014/05/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A novel general approximation scheme (NGAS) proposed earlier (ref.2-3) is applied to the problem of the quartic anharmonic (QAHO) and the double-well-oscillator (QDWO) in quantum theory by choosing the infinite square-well-potential in one dimension as the input approximation. The leading order (LO) results obtained for the energy eigen-values are uniformly accurate to within a few percent of the exact results for arbitrary values of the quartic coupling: λ> 0 and the level-index n_s. These results are shown to be non-perturbative in the LO and reproduce the known analytic and scaling properties of energy as a function of the coupling λ and n_s. The LO-results are further improved in accuracy by including the perturbative-correction at the next non-trivial order of an improved perturbation theory (IPT) based upon NGAS. The method can be trivially extended to other cases of higher anharmonicity.

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