Application of finite‐element method to the two‐dimensional Schrödinger equation

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Abstract
An algorithm to solve the two‐dimensional Schrödinger equation based on the finite‐element method is proposed. In our scheme, the molecular Hamiltonian with any arbitrary internal coordinate system can be solved as easily as with the Cartesian coordinate system. The efficient computer program based on the algorithm was developed on the HITAC S‐810 supercomputer. The performance of the program is examined in the following test problems; (1) free particle in a box, (2) linear triatomic molecule with two equal force constants, (3) coupled Morse oscillators, (4) Henon‐Heiles potential, (5) H3O+ symmetric vibrational modes. The algorithm is demonstrated to be very suited for the vector‐type supercomputer.