New useful special function in quantum optics theory

Feng Chen, Hong-Yi Fan

By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e., By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators (IWOP) we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.

Klaus M. Gheri, Daniel F. Walls

J. M. Vigoureux

I show that the reflection coefficient of any stratified planar structure can be obtained by using a complex generalization of Einstein's addition theorem for parallel velocities. This result also applies to multiple quantum wells. It provides a new mathematical tool in optics and in quantum theory and may lead to useful algorithms in computing. It may also give a new insight into special relativity. The composition law of velocities, in fact, no longer appears as a specific result of special relativity but rather as the expression, in the particular case of kinematics, of a more general law of physics. The possible use of the composition law of probability amplitude in quantum theory is also presented.

Ravinder Rupchand Puri

Hai-jun Yu, Zhong Guo-Bao, MA Jian-guo +1 more

Inspired by the wavelet transform in quantum mechanics, we define the new Ridgelet transform for quantum optics by rewriting the classic Ridgelet transform via the two-mode coordinate representation in Fock space. Furthermore, we give the explicit form of the asymmetric operator's integral and derive two useful formulas for the normal ordering of the two-mode operator with the help of the technique of integration within an ordered product (IWOP) of operators. By choosing the two-variable Mexican hat's mother wavelet function, we analyse the Ridgelet transforms of the coherent state, special squeezed coherent state, intermediary entangled state on the basis of the theories we have mentioned.

Marlan O. Scully, Kenneth G. Whitney