Mapped Finite Element Discrete Variable Representation

Efficient numerical solver for the Schr?dinger equation is very important in physics and chem-istry. 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 ³∑³_gof the Cs₂ molecule which has long-range interaction potential. The numerical results indicate that the numeri-cal efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme