Abstract

The quantum-mechanical problem of the nonlinear oscillator with the Lagrangian L= 1/2 [x2-k0x2)/(l-λx2)] is solved exactly and the energy levels and eigenfunctions are obtained completely. This model (whenk0=0) is the zero-space-dimensional isoscalar analogue of the nonlinearSU2⊗ SU2 chirally invariant Lagrangian in the Gasiorowicz-Geffen co-ordinates and may also be considered as a modified version of the anharmonic-oscillator and Lee-Zumino models. The bound-state energy levels are found to have a linear dependence on the coupling parameter, in sharp contrast to the case of the familiar oscillator With quartic anharmonicity where the energy, as a function of λ, has complicated singularities at λ = 0. We investigate how far certain standard approximation procedures reproduce the exact results. The Bohr-Sommerfeld quantization procedure is found to reproduce the form of the boundstate energy levels correctly. Interestingly a perturbation-theoretic treatment also reproduces the correct results at least up to the order (λ2) to which we have carried our calculations.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call