On Feynman method of disentangling of noncommuting operators

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 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.