# A complex guided spectral transform Lanczos method for studying quantum resonance states

## Abstract

A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths, and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore, the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO{sub 2}, and compared to previous calculations.

- Authors:

- Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973-5000 (United States)

- Publication Date:

- OSTI Identifier:
- 22415411

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 24; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; COMPARATIVE EVALUATIONS; EIGENSTATES; ENERGY LEVELS; HAMILTONIANS; LAYERS; POLYNOMIALS; QUANTUM STATES; SURFACES; SYMMETRY; WAVE FUNCTIONS

### Citation Formats

```
Yu, Hua-Gen, E-mail: hgy@bnl.gov.
```*A complex guided spectral transform Lanczos method for studying quantum resonance states*. United States: N. p., 2014.
Web. doi:10.1063/1.4905083.

```
Yu, Hua-Gen, E-mail: hgy@bnl.gov.
```*A complex guided spectral transform Lanczos method for studying quantum resonance states*. United States. doi:10.1063/1.4905083.

```
Yu, Hua-Gen, E-mail: hgy@bnl.gov. Sun .
"A complex guided spectral transform Lanczos method for studying quantum resonance states". United States.
doi:10.1063/1.4905083.
```

```
@article{osti_22415411,
```

title = {A complex guided spectral transform Lanczos method for studying quantum resonance states},

author = {Yu, Hua-Gen, E-mail: hgy@bnl.gov},

abstractNote = {A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths, and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore, the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO{sub 2}, and compared to previous calculations.},

doi = {10.1063/1.4905083},

journal = {Journal of Chemical Physics},

number = 24,

volume = 141,

place = {United States},

year = {Sun Dec 28 00:00:00 EST 2014},

month = {Sun Dec 28 00:00:00 EST 2014}

}