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On Feynman method of disentangling of noncommuting operators. (English) Zbl 1222.81116

Summary: The Feynman method of disentangling of noncommuting operators is applied to the problem of quantum oscillator with variable frequency. It is shown that this problem is mathematically equivalent to rotation of pseudospin in quasiunitary group \(\text{SU}(1,1)\). The oscillator states form a basis for unitary irreducible representations of this group. Combining group-theoretical considerations with the Feynman method, we obtain simple analytic formulae for transition probabilities between initial and final oscillator states. The Feynman method is also applied to the Hamiltonian of atom or ion in laser field.

MSC:

81P15 Quantum measurement theory, state operations, state preparations
81V80 Quantum optics
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References:

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