Abstract
A more exact formulation for Dirac’s proposition on the analogy between the unitary transformations in quantum theory and the contact transformations in classical theory is given. It is shown that approximate expressions for the matrix elements of the unitary operator defining the transformation can be constructed in terms of classical quantities. One can thus speak not only of an analogy between unitary and contact transformations, but also of an approximate equality between the quantum mechanical and semi-classical expressions for the corresponding quantities.
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Уточнено утверждение Дирака об аналогии между унитарными преобразовани. ями квантовой механики и касательными преобразованиями классической механики-Показано, что для матричных элементов оператора унитарного преобразования могут быть построены приближенные выражения через классические величины. Таким образом можно говорить не только об аналогии между унитарными и касательными преобразованиями, но и о приближенном равенстве между квантово-механическими и полу-классическими выражениями для соответствующих величин.
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Dedicated to Prof.P. Gombás on his 60th birthday.
First published in Russian in the Bulletin (Viestnik) of the Leningrad University, No 16, p. 67, 1959. See also Appendix to the Russian edition ofDirac’s book “The Principles of Quantum Mechanics”, Moscow, 1960. The present English text prepared for Acta Physica Hungarica has been partly revised by the author.
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Fock, V. On the canonical transformation in classical and quantum mechanics. Acta Physica 27, 219–224 (1969). https://doi.org/10.1007/BF03156744
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DOI: https://doi.org/10.1007/BF03156744