Coherent and incoherent superposition of transition matrix elements of the squeezing operator

Abstract We discuss the general matrix elements of squeezing operator between number eigenstates a harmonic oscillator (which may also represent quantized mode electromagnetic radiation). These have first been used by Popov and Perelomov (1969) long ago, in their thorough analysis parametric excitation oscillators. They expressed terms transcendental functions, associated Legendre functions. In present paper we will show that these can be derived an different form, classical Gegenbauer polynomials. This new expression makes it possible to determine coherent incoherent superpositions closed analytic forms. As application, describe multiphoton transitions system “charged particle + radiation”, induced (strong) field or black-body radiation component (with Planck-Bose photon distribution). The exact results are compared with semi-classical ones. case interaction thermal field, result Gaussian stochastic amplitude) yields acceptable approximation only Rayleigh-Jeans limit, however, Wien limit completely fails.