The shape invariant symmetry of the Trigonometric Rosen-Morse and Eckart potentials has been studied through realization of so（3） and so（2, 1） Lie algebras respectively. In this work, by using the free particle ei...The shape invariant symmetry of the Trigonometric Rosen-Morse and Eckart potentials has been studied through realization of so（3） and so（2, 1） Lie algebras respectively. In this work, by using the free particle eigenfunction, we obtain continuous spectrum of these potentials by means of their shape invariance symmetry in an algebraic method.展开更多
The one dimensional Schrodinger equation associated with a time-dependent Morse potentials is studied. We use the invariant operator method （Lewis and Riesenfeld） to obtain approximate solution of the Schrodinger eq...The one dimensional Schrodinger equation associated with a time-dependent Morse potentials is studied. We use the invariant operator method （Lewis and Riesenfeld） to obtain approximate solution of the Schrodinger equation in terms of solution of second order ordinary differential equation describes the amplitude of the Morse potentials.展开更多
This paper studies the Gauss map of submanifolds in space forms defined by Willmore andSaleemi. By using Morse functions,it is proved that the degree of Gauss map is the Eulernumber of the submanifold.The tight immers...This paper studies the Gauss map of submanifolds in space forms defined by Willmore andSaleemi. By using Morse functions,it is proved that the degree of Gauss map is the Eulernumber of the submanifold.The tight immersions are also studied.展开更多
文摘The shape invariant symmetry of the Trigonometric Rosen-Morse and Eckart potentials has been studied through realization of so（3） and so（2, 1） Lie algebras respectively. In this work, by using the free particle eigenfunction, we obtain continuous spectrum of these potentials by means of their shape invariance symmetry in an algebraic method.
文摘The one dimensional Schrodinger equation associated with a time-dependent Morse potentials is studied. We use the invariant operator method （Lewis and Riesenfeld） to obtain approximate solution of the Schrodinger equation in terms of solution of second order ordinary differential equation describes the amplitude of the Morse potentials.
文摘This paper studies the Gauss map of submanifolds in space forms defined by Willmore andSaleemi. By using Morse functions,it is proved that the degree of Gauss map is the Eulernumber of the submanifold.The tight immersions are also studied.
