Abstract
Efficient numerical solver for the Schrödinger equation is very important in physics and chemistry. The finite element discrete variable representation (FE-DVR) was first proposed by Rescigno and Mc-Curdy [Phys. Rev. A 62, 032706 (2000)] for solving quantum-mechanical scattering problems. In this work, an FE-DVR method in a mapped coordinate was proposed to improve the efficiency of the original FE-DVR method. For numerical demonstration, the proposed approach is applied for solving the electronic eigenfunctions and eigenvalues of the hydrogen atom and vibrational states of the electronic state 3Σg+ of the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numerical efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme.
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