The power law and the logarithmic potentials. (English) Zbl 1046.81510
Summary: We show that the energy eigenvalues and the eigenfunctions of the Schrödinger equation for the power law and the logarithmic potentials can be easily obtained by using a variation technique for special type wavefunctions. The results are in very good agreement with exact numerical results.
MSC:
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
35J10 | Schrödinger operator, Schrödinger equation |