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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Matrix elements of Bogolubov canonical transformations

Evelyn Aronson, I.A. Malkin, Vladimir I. Man’ko

Published Sep 1, 1974• 7 citations
Publisher
DOI
10.1007/bf02752726

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Sufficient conditions are given for the possibility to construct quantum mechanical wavefunctions by the sole knowledge of an appropriate sequence of classical canonical transformations which map a given Hamiltonian onto the new position variable. The transformation matrix element for each individual step of this sequence is given by the semiclassical limit expression of these matrix elements; it is a function of the generator of this transformation step only. The wavefunction, i.e. the transformation matrix element for the total transformation, is obtained as a multiple integral over the transformation matrix elements of the various intermediate steps. The practicability of this procedure is demonstrated by several examples. The authors consider time-independent systems with one degree of freedom.