Solution of the time dependent Schroedinger equation at a given potential

Barry I. Schneider, Lee A. Collins

Jay Sharon Bolemon, Stephen B. Haley

Chao‐Yun Long, Shuijie Qin, Zhu-Hua Yang +1 more

S. D. Bajpai, Debahuti Mishra

One of the fundamental problems in quantum mechanics is to find a solution of Schroedinger equation for different forms of potentials. The object of this paper is to obtain a series solution of a particular one-dimensional, time-dependent Schroedinger equation involving Hermite polynomials. The authors also show a relationship of their particular one-dimensional, time-dependent Schroedinger equation with an equation of heat conduction.

Babur M. Mirza

We investigate wavepacket solutions for time-dependent Schoedinger equation in the presence of an exponentially decaying potential. Assuming for travelling wave solutions the phase to be a linear combination of the space and time coordinates, we obtain two distinct wavepacket solutions for the Schroedinger equation. The wavepackets counterpropagate in space at a constant velocity without any distortion or spreading thus retain their initial form at arbitrarily large distances.