# Time-dependent Schroedinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations

## Abstract

In this paper, we focus on a general class of Schroedinger equations that are time dependent and quadratic in X and P. We transform Schroedinger equations in this class, via a class of time-dependent mass equations, to a class of solvable time-dependent oscillator equations. This transformation consists of a unitary transformation and a change in the ''time'' variable. We derive mathematical constraints for the transformation and introduce two examples. (c) 2000 American Institute of Physics.

- Authors:

- Theoretical Division (MS-B285), Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545 (United States)
- Department of Chemistry, University of Calgary, Calgary, Alberta T2N 1N4, (Canada)

- Publication Date:

- OSTI Identifier:
- 20216305

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 41; Journal Issue: 5; Other Information: PBD: May 2000; Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SCHROEDINGER EQUATION; SYMMETRY GROUPS; ALGEBRA; TRANSFORMATIONS; HAMILTONIANS; THEORETICAL DATA

### Citation Formats

```
Nieto, Michael Martin, and Truax, D. Rodney.
```*Time-dependent Schroedinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations*. United States: N. p., 2000.
Web. doi:10.1063/1.533268.

```
Nieto, Michael Martin, & Truax, D. Rodney.
```*Time-dependent Schroedinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations*. United States. doi:10.1063/1.533268.

```
Nieto, Michael Martin, and Truax, D. Rodney. Mon .
"Time-dependent Schroedinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations". United States. doi:10.1063/1.533268.
```

```
@article{osti_20216305,
```

title = {Time-dependent Schroedinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations},

author = {Nieto, Michael Martin and Truax, D. Rodney},

abstractNote = {In this paper, we focus on a general class of Schroedinger equations that are time dependent and quadratic in X and P. We transform Schroedinger equations in this class, via a class of time-dependent mass equations, to a class of solvable time-dependent oscillator equations. This transformation consists of a unitary transformation and a change in the ''time'' variable. We derive mathematical constraints for the transformation and introduce two examples. (c) 2000 American Institute of Physics.},

doi = {10.1063/1.533268},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 5,

volume = 41,

place = {United States},

year = {2000},

month = {5}

}

DOI: 10.1063/1.533268

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