Abstract
In this article, the Davydov-Chaban Hamiltonian for collective motion of atomic nuclei by considering the rigidity at $\gamma=30^{\circ}$ with a time-dependent interaction has been studied. Throughout this article, the Lewis-Riesenfeld dynamical invariant method has been used, that enables us to derive the wave function of our considered system which has explicit time dependence. Derivation of the Lewis-Riesenfeld dynamical invariant has been mentioned in detail. After deriving the eigen values and functions, the wave functions have been derived according to the eigen functions of the Lewis-Riesenfeld dynamical invariant. Some discussions about our results have been done in the last part of this paper.
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