arXiv subjects
Publications and source records attributed to Zhao Wei-Qin.
Based on two different iteration procedures the groundstate wave functions and energies for N-dimensional generalized Sombrero-shaped potentials are solved. Two kinds of trial functions for the iteration procedure are defined. The iterative solutions are convergent nicely to consistent results for different choices of iteration procedures and trial functions.
Based on an iterative method for solving the goundstate of Schroedinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.
It is proved that when solving Schroedinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower dimensional cases. This result is applied to giving solutions for several radially symmetric potentials in N-dimension.
A revised new iterative method based on Green function defined by quadratures along a single trajectory is developed and applied to solve the ground state of the double-well potential. The result is compared to the one based on the original iterative method. The limitation of the asymptotic expansion is also discussed.
A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schroedinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.