Generalized Adiabatic Invariance
Open Access
- 1 March 1964
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 5 (3), 355-362
- https://doi.org/10.1063/1.1704127
Abstract
In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m - 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally)Keywords
This publication has 15 references indexed in Scilit:
- General Theory of Perturbations in Classical MechanicsProceedings of the Physical Society, 1963
- Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly PeriodicJournal of Mathematical Physics, 1962
- Degree of approximate validity of the adiabatic invariance in quantum mechanicsPhysica, 1962
- Action principle for classical mechanicsJournal of Mathematical Analysis and Applications, 1961
- Perturbations in Classical MechanicsProceedings of the Physical Society, 1960
- An extended adiabatic invariantJournal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, 1960
- Adiabatic Invariants of Periodic Classical SystemsPhysical Review B, 1959
- Adiabatic invariance to all ordersAnnals of Physics, 1959
- On the Convergence of the Perturbation Method, II. 1Progress of Theoretical Physics, 1950
- Zur Operatorenmethode In Der Klassischen MechanikAnnals of Mathematics, 1932