Eigenvalues of λx2m anharmonic oscillators

Biswas, S. N. ; Datta, K. ; Saxena, R. P. ; Srivastava, P. K. ; Varma, V. S. (1973) Eigenvalues of λx2m anharmonic oscillators Journal of Mathematical Physics, 14 (9). pp. 1190-1195. ISSN 0022-2488

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Official URL: http://link.aip.org/link/jmapaq/v14/i9/p1190/s1

Related URL: http://dx.doi.org/10.1063/1.1666462


The ground state as well as excited energy levels of the generalized anharmonic oscillator defined by the Hamiltonian Hm = - d2/dx2+x2+ λx2m, m = 2,3,..., have been calculated nonperturbatively using the Hill determinants. For the λx4 oscillator, the ground state eigenvalues, for various values of λ, have been compared with the Borel-Pade sum of the asymptotic perturbation series for the problem. The agreement is excellent. In addition, we present results for some excited states for m = 2 as well as the ground and the first even excited states for m = 3 and 4. The behaviour of all the energy levels with respect to the coupling parameter shows a qualitative similarity to the ground state of the λx4 oscillator. Thus the results are model independent, as is to be expected from the WKB approximation. Our results also satisfy the scaling property that εn(m)(λ)/λ1/(m+1) tend to a finite limit for large λ, and always lie within the variational bounds, where available.

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Deposited On:06 Dec 2010 12:44
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