# Dynamical symmetry approach to periodic Hamiltonians

## Abstract

We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and find that the complementary series plays a central role as well as nonunitary representations. (c) 2000 American Institute of Physics.

- Authors:

- Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520-8120 (United States)

- Publication Date:

- OSTI Identifier:
- 20216304

- 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; HAMILTONIANS; DYNAMICAL GROUPS; SYMMETRY GROUPS; SU GROUPS; SO GROUPS; LIE GROUPS; TRANSFER MATRIX METHOD; DISPERSION RELATIONS; POTENTIAL ENERGY; THEORETICAL DATA

### Citation Formats

```
Li, Hui, and Kusnezov, Dimitri.
```*Dynamical symmetry approach to periodic Hamiltonians*. United States: N. p., 2000.
Web. doi:10.1063/1.533265.

```
Li, Hui, & Kusnezov, Dimitri.
```*Dynamical symmetry approach to periodic Hamiltonians*. United States. doi:10.1063/1.533265.

```
Li, Hui, and Kusnezov, Dimitri. Mon .
"Dynamical symmetry approach to periodic Hamiltonians". United States. doi:10.1063/1.533265.
```

```
@article{osti_20216304,
```

title = {Dynamical symmetry approach to periodic Hamiltonians},

author = {Li, Hui and Kusnezov, Dimitri},

abstractNote = {We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and find that the complementary series plays a central role as well as nonunitary representations. (c) 2000 American Institute of Physics.},

doi = {10.1063/1.533265},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 5,

volume = 41,

place = {United States},

year = {2000},

month = {5}

}

DOI: 10.1063/1.533265

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