Schr�dinger equations for su q (2)-invariant quantum systems

Mich�le Irac-Astaud

Jiangfan Li, Shan Shu-min, Yang Jian-Kun +2 more

The time-dependent invariant of a quantum frequency conversion system in an optical cavity is found from the simple observation that the dynamical evolution of a sum-frequency generation process preserves the total number of the idler photons and the signal photons involved in the process. By using this invariant and the Lewis-Riesenfeld quantum invariant approach, the Schrdinger equation for the coupled system of the two quantized modes of the electromagnetic field is solved under detuned condition. The explicitly analytical formulae of the quantum states and the evolution operators of the system are obtained. It should be useful for further studies on the various quantum properties of the quantum system.

Swarnamala Sirsi, Veena Adiga

Nikhil Singh

Erwin Schr & #214;dinger is considered one of the founding father of quantum mechanics. Schr & #214;dinger's equation is fundamental of understanding Quantum Mechanics. Laws of Newtonian system don't work in quantum system. In this Research paper I have discussed brief overview on Schr & #214;dinger's wave equation.

Mich�le Irac-Astaud, C. Quesne

Feng Jin

The two quantum invariant operators are constructed from the time dependent Harmiltonian of the harmonic oscillator with an auxiliary condition. The solution of the Schrdinger equation for the system is derived by using these invariant operators.