In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arb...In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.展开更多
Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region.Usually it works effectively but becomes inefficient when the wave function in...Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region.Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range,particularly involving ultra-low energy.In this work,a new transparent boundary condition(TBC)is proposed for the time-dependent wave packet method.It in principle is of spectral accuracy when typical discrete variable representations are applied.The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function,in contrast with the complex absorbing potential.Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well,which supports resonances states.展开更多
基金This work was supported by the National Basic Research Program of China （No.2013CB922200）, the National Natural Science Foundation of China （No.21222308, No.21103187, and No.21133006）, the Chinese Academy of Sciences, and the Key Research Program of the Chinese Academy of Sciences.
文摘In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.
基金supported by the National Natural Science Foundation of China (No.21733006,No.21825303 and No.21688102)the Strategic Priority Research Program of Chinese Academy of Sciences (No.XDB17010200).
文摘Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region.Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range,particularly involving ultra-low energy.In this work,a new transparent boundary condition(TBC)is proposed for the time-dependent wave packet method.It in principle is of spectral accuracy when typical discrete variable representations are applied.The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function,in contrast with the complex absorbing potential.Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well,which supports resonances states.
