Quantum Propagator for Arbitrary Potentials on General Grids
LIN Shang1, HE Chun-Long1, LI Jia-Ming1
1Department of Physics, Shanghai Jiaotong University, Shanghai 200030
2Center for Atomic and Molecular Nanosciences, Department of Physics, Tsinghua University, Beijing 100084
3Institute of Physics, Chinese Academy of Sciences, Beijing 100080
Quantum Propagator for Arbitrary Potentials on General Grids
LIN Shang1;HE Chun-Long1;LI Jia-Ming1
1Department of Physics, Shanghai Jiaotong University, Shanghai 200030
2Center for Atomic and Molecular Nanosciences, Department of Physics, Tsinghua University, Beijing 100084
3Institute of Physics, Chinese Academy of Sciences, Beijing 100080
Abstract： The point-to-point Feynman quantum propagator < q1|exp(-iHt/ħ)|q2> has an analytic
form only for quadratic potentials. We apply the split operator approach to obtain a propagator matrix for arbitrary potentials for non-uniform grids, which are particularly useful for real physical potentials with both rapid-varying and smooth regions. We exemplify our method with the wavefunction propagation and the extraction of an eigenvalue and an eigenfunction of a Morse system modelling diatomic molecules.
LIN Shang;HE Chun-Long;LI Jia-Ming. Quantum Propagator for Arbitrary Potentials on General Grids[J]. 中国物理快报, 2004, 21(4): 644-647.
LIN Shang, HE Chun-Long, LI Jia-Ming. Quantum Propagator for Arbitrary Potentials on General Grids. Chin. Phys. Lett., 2004, 21(4): 644-647.
2004, Vol. 21 
