### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 1491-1497 |

Number of pages | 7 |

Journal | The Journal of chemical physics |

Volume | 103 |

Issue number | 4 |

State | Published - 1995 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of chemical physics*,

*103*(4), 1491-1497.

**Noise-free spectrum for time-dependent calculation of eigenenergies.** / Dai, Jiqiong; Zhang, John.

Research output: Contribution to journal › Article

*The Journal of chemical physics*, vol. 103, no. 4, pp. 1491-1497.

}

TY - JOUR

T1 - Noise-free spectrum for time-dependent calculation of eigenenergies

AU - Dai, Jiqiong

AU - Zhang, John

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000864216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000864216&partnerID=8YFLogxK

M3 - Article

VL - 103

SP - 1491

EP - 1497

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 4

ER -