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1964

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/24547

Generalized adiabatic invariance

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http://dx.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).

Subject

Teoria quàntica, Espais de Hilbert, Pertorbació (Dinàmica quàntica)

Subject (English)

Quantum theory, Hilbert space, Perturbation (Quantum dynamics)

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Articles publicats en revistes (Física de la Matèria Condensada)

Citation

GARRIDO, L. (Luis). Generalized adiabatic invariance. Journal of Mathematical Physics. 1964. Vol. 5, num. 355. ISSN 0022-2488. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/24547

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