# Linear-least-squares fitting method for the solution of the time-dependent Schroedinger equation: Applications to atoms in intense laser fields

## Abstract

An alternative theoretical approach for solving the time-dependent Schroedinger equation for atoms in an intense laser field is presented. In this method the time-dependent wave function is expanded in a basis set but the expansion coefficients are determined by linear-least-squares fitting of the wave function on discrete mesh points in configuration space, thus avoiding the need of evaluating a large number of matrix elements. We illustrate the method by computing wave functions, above-threshold ionization spectra, and harmonic generation spectra of a model atom and compare the results with those obtained using the split-operator method. (c) 2000 The American Physical Society.

- Authors:

- Department of Physics, Kansas State University, Manhattan, Kansas 66506-2601 (United States)
- (China)

- Publication Date:

- OSTI Identifier:
- 20216406

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 5; Other Information: PBD: May 2000; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; SCHROEDINGER EQUATION; PHOTON-ATOM COLLISIONS; WAVE FUNCTIONS; QUANTUM MECHANICS; PHOTOIONIZATION; RADIATION PRESSURE; HARMONIC GENERATION; LEAST SQUARE FIT; THEORETICAL DATA

### Citation Formats

```
Zhou, Xiaoxin, Department of Physics, Northwest Normal University, Lanzhou, Ganzu, 730070, People's Republic of China and Wuhan Institute of Physics, Chinese Academy of Sciences, Wuhan, 430071, People's Republic of China, and Lin, C. D.
```*Linear-least-squares fitting method for the solution of the time-dependent Schroedinger equation: Applications to atoms in intense laser fields*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevA.61.053411.

```
Zhou, Xiaoxin, Department of Physics, Northwest Normal University, Lanzhou, Ganzu, 730070, People's Republic of China and Wuhan Institute of Physics, Chinese Academy of Sciences, Wuhan, 430071, People's Republic of China, & Lin, C. D.
```*Linear-least-squares fitting method for the solution of the time-dependent Schroedinger equation: Applications to atoms in intense laser fields*. United States. doi:10.1103/PhysRevA.61.053411.

```
Zhou, Xiaoxin, Department of Physics, Northwest Normal University, Lanzhou, Ganzu, 730070, People's Republic of China and Wuhan Institute of Physics, Chinese Academy of Sciences, Wuhan, 430071, People's Republic of China, and Lin, C. D. Mon .
"Linear-least-squares fitting method for the solution of the time-dependent Schroedinger equation: Applications to atoms in intense laser fields". United States. doi:10.1103/PhysRevA.61.053411.
```

```
@article{osti_20216406,
```

title = {Linear-least-squares fitting method for the solution of the time-dependent Schroedinger equation: Applications to atoms in intense laser fields},

author = {Zhou, Xiaoxin and Department of Physics, Northwest Normal University, Lanzhou, Ganzu, 730070, People's Republic of China and Wuhan Institute of Physics, Chinese Academy of Sciences, Wuhan, 430071, People's Republic of China and Lin, C. D.},

abstractNote = {An alternative theoretical approach for solving the time-dependent Schroedinger equation for atoms in an intense laser field is presented. In this method the time-dependent wave function is expanded in a basis set but the expansion coefficients are determined by linear-least-squares fitting of the wave function on discrete mesh points in configuration space, thus avoiding the need of evaluating a large number of matrix elements. We illustrate the method by computing wave functions, above-threshold ionization spectra, and harmonic generation spectra of a model atom and compare the results with those obtained using the split-operator method. (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevA.61.053411},

journal = {Physical Review. A},

issn = {1050-2947},

number = 5,

volume = 61,

place = {United States},

year = {2000},

month = {5}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.