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Simple relationship between energy and adiabatic invariants for systems with a power‐law potential

 

作者: A. M. Cetto,   L. de la Peña,  

 

期刊: American Journal of Physics  （AIP Available online 1984）
卷期: Volume 52, issue 6  

页码: 539-542

 

ISSN:0002-9505

 

年代: 1984

 

DOI:10.1119/1.13615

 

出版商: American Association of Physics Teachers

 

关键词: classical mechanics;quantum mechanics;semiclassical approximation;perturbation theory;hamiltonians;energy;adiabatic invariance;one−dimensional systems;harmonic oscillators;virial theorem

 

数据来源: AIP

 

摘要:

A simple relation between the energyEand the adiabatic invariantJis derived for Hamiltonian systems with a potentialV=axkby making use of the virial theorem. By further developing a first‐order perturbation technique one arrives at a modified expression for the energy in terms ofJforV=axk+bxl. The results obtained are valid in classical mechanics, as well as in the semiclassical domain of quantum mechanics.

 

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