# Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states

## Abstract

Using the transformations from paper I, we show that the Schroedinger equations for (1) systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is demonstrated. (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:
- 20216306

- 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; LIE GROUPS; THEORETICAL DATA

### Citation Formats

```
Nieto, Michael Martin, and Truax, D. Rodney.
```*Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states*. United States: N. p., 2000.
Web. doi:10.1063/1.533269.

```
Nieto, Michael Martin, & Truax, D. Rodney.
```*Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states*. United States. doi:10.1063/1.533269.

```
Nieto, Michael Martin, and Truax, D. Rodney. Mon .
"Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states". United States. doi:10.1063/1.533269.
```

```
@article{osti_20216306,
```

title = {Time-dependent Schroedinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states},

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

abstractNote = {Using the transformations from paper I, we show that the Schroedinger equations for (1) systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is demonstrated. (c) 2000 American Institute of Physics.},

doi = {10.1063/1.533269},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 5,

volume = 41,

place = {United States},

year = {2000},

month = {5}

}

DOI: 10.1063/1.533269

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