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Some remarks on the unitary time evolution operator of the quantum-mechanical forced oscillator. The Weierstrass propagator

Замечания об унитарном операторе временной эволюции квантовомеханического вынужденного осциллятора. Пропагатор Веиерштрасса

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Il Nuovo Cimento B (1971-1996)

Summary

The convergence properties of the unitary time evolution operator of the quantum-mechanical forced oscillator are investigated in some detail. On using the inversion of the Weierstrass transform, the propagator of this system is obtained, from which a complete set of square integrable solutions is generated.

Riassunto

Si studiano in dettaglio le proprietà di convergenza dell'operatore unitario di evoluzione nel tempo dell'oscillatore forzato quantomeccanico. Usando l'inversione della transformazione di Weierstrass, si ottiene il propagatore di questo sistema, dal quale è generata una serie completa di soluzioni integrabili al quadrato.

Резюме

Подробно исследуются свойства сходимости унитарного оператора временной эволюции квантовомеханического вынужденного осциллятора. Используя инверсию преобразования Вейерштрасса, получается пропагатор такой системы, из которого определяется полная система квадратично интегрируемых решений.

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References

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Author notes

  1. H. Grinberg

    Present address: The Jones Frank Institute, The University of Chicago, 60637, Chicago, Ill., U.S.A.

Authors and Affiliations

  1. Laboratorio de Física Teórica, Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. No. 67, (1900), La Plata, República Argentina

    H. Grinberg

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  1. H. Grinberg
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Grinberg, H. Some remarks on the unitary time evolution operator of the quantum-mechanical forced oscillator. The Weierstrass propagator. Nuov Cim B 83, 17–22 (1984). https://doi.org/10.1007/BF02723760

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  • DOI: https://doi.org/10.1007/BF02723760

PACS. 03.65

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