With the help of the evolution operator method, we have established unitary connection between quadratic systems, namely between a free particle with variable mass M(t) , a particle with variable mass M(t) in a variable homogeneous field, and a harmonic oscillator with variable mass M(t) and frequency ω(t) , on which a variable force F(t) acts. Knowledge of the unitary connection allowed us to express easily in general form the propagators, invariants, wave functions, and other functions of a linear potential and a harmonic oscillator in terms of the corresponding quantities for a free particle. We have analyzed the linear and quadratic invariants in detail. Results known in the literature follow as particular cases from the general results obtained here.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 27–38, December, 2018.
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Nagiyev, S.M., Ahmadov, A.I., Tarverdiyeva, V.A. et al. Regarding Nonstationary Quadratic Quantum Systems. Russ Phys J 61, 2173–2187 (2019). https://doi.org/10.1007/s11182-019-01654-7
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DOI: https://doi.org/10.1007/s11182-019-01654-7