On the energy spectra of one dimensional and harmonic oscillators

Mathews, P. M. ; Seetharaman, M. ; Raghavan, Sekhar ; Bhargava, V. T. A. (1981) On the energy spectra of one dimensional and harmonic oscillators Pramana - Journal of Physics, 17 (2). pp. 121-134. ISSN 0304-4289

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Official URL: http://www.ias.ac.in/j_archive/pramana/17/2/121-13...


In this paper we present explicit and simple analytical formulae for the energy eigenvalues En(λ) of one-dimesional anharmonic oscillators characterized by the potentials ½mω2x2+λx with α = 2, 3 and 4. A simple intuitive criterion supplemented by the requirment of correct asymptotic behavour, has been employed in arriving at the formulae. Our energy values over a wide range of n and λ are in good agreement with the numerical values computed by earlier workers through very elaborate techniques. To our knowledge this is the first time that formulae of such wide validity have been given. The results of pure power oscillators are rivally obtained by going over to the ω→0 limet. Approximate analytic expressions for th low order even moment of x are also given.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Anharmonic Oscillator; Renormalized Frequency; Energy Eigenvalue Moments
ID Code:81185
Deposited On:04 Feb 2012 11:27
Last Modified:18 May 2016 22:51

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