We explored and studied the use of several energy spectra for numerical applications in time-dependent calculation of bound state energies. Although all three types of the spectrum we studied, Sinc, Lorentzian, and Gaussian, approach the δ-function limit in the infinite time limit, their numerical properties at finite time limit are quite different. Our analysis, supported by numerical example, shows that by using Gaussian or Lorentzian spectrum, one can eliminate all the "noises" (extra peaks) present in the standard Sinc spectrum based on Fourier transform of autocorrelation function. The use of these two spectra enables us to obtain unambiguously all eigenvalues as long as the corresponding eigenfunctions have overlaps, albeit small, with the initial wavepacket. These small-component eigenstates are normally buried under the spectral "noise" in the standard Sinc spectrum. The Gaussian spectrum offers better resolution than Lorentzian spectrum and is recommended for use in time-dependent calculation of eigenenergies.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry