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00925njm 22002777a 4500 dc Garrido, L. (Luis), 1930-2009 author 2012-04-26T09:36:37Z 2012-04-26T09:36:37Z 1964 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). Teoria quàntica Espais de Hilbert Pertorbació (Dinàmica quàntica) Quantum theory Hilbert space Perturbation (Quantum dynamics) Generalized adiabatic invariance