Bibliographic Details
| Title: |
Quasi exact solutions for an asymmetric double well potential. |
| Authors: |
Burrows, B. L., Cohen, M., Feldmann, Tova |
| Source: |
Molecular Physics. 6/20/96, Vol. 88 Issue 3, p611-620. 10p. |
| Subjects: |
Quantum wells, Potential theory (Physics) |
| Abstract: |
Algebraic methods are used to derive approximate quasi exact solutions for a parametric model potential having the functional form V(x) = V0 - Mbetax + 1/2x2(alpha + betax)2 with M a positive integer and beta > 0. This yields an asymmetric double well potential provided that the parameters (M, alpha, beta) satisfy the conditions -1/12 3 < omega = - Mbeta2/2alpha3 < 1/12 3. If k = alpha2/beta is sufficiently large there is a high barrier between the two wells, and the quasi exact spectrum is essentially harmonic. More generally, each quasi exact solution is the product of a finite polynomial and a universal asymptotic factor, exp[-(1/2alphax2 + 1/3betax3)], and is mainly localized in the deeper well, even when the spectrum is significantly non-harmonic. For omega sufficiently small, both the quasi exact spectrum and the lower excited bound state spectrum are determined quite accurately by low order Rayleigh-Schrodinger perturbation theory following a suitable (but non-standard) canonical transformation of the reduced Hamiltonian. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
