Classical and Quantum Oscillators of Sextic and Octic Anharmonicities

Details Classical and Quantum Oscillators of Sextic and Octic Anharmonicities Classical and Quantum Oscillators of Sextic and Octic Anharmonicities

2002-06-03

arxiv.org/abs/quant-ph/0206011v1

Physics

Quantum Physics

13 pages, latex 2e, 1 figure Journal Reference: Phys. Lett. A (2002) in press

Scientific paper

10.1016/S0375-9601(02)00500-5

Classical oscillators of sextic and octic anharmonicities are solved analytically up to the linear power of \lambda (Anharmonic Constant) by using Taylor series method. These solutions exhibit the presence of secular terms which are summed up for all orders. The frequency shifts of the oscillators for small anharmonic constants are obtained. It is found that the calculated shifts agree nicely with the available results to-date. The solutions for classical anharmonic oscillators are used to obtain the solutions corresponding to quantum anharmonic oscillators by imposing fundamental commutation relations between position and momentum operators.

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