香蕉视频

Title:Time-dependent exactly solvable potentials generated by Darboux and point transformations.

Abstract:The appropriate form-preserving point transformation is introduced to deform a given stationary Schr枚dinger equation into one with a time-dependent potential. The solutions for the new model are inherited from the stationary system and form an orthogonal set. The latter is guaranteed from the preservation of the inner product. The constants of motion (invariant operators) are extracted in a straightforward form by simply performing the appropriate mapping and exploiting the preservation of the 铿乺st integrals available in the initial model. In particular, it is shown that the parametric oscillator can be obtained as a deformation of the harmonic oscillator. Lastly, a new family of time-dependent potentials is generated after combining the Darboux and point transformations, leading to a generalization of the Abraham-Moses-Mielnik potential.