A unified algebraic approach to bound and continuum states of anharmonic potentials

✍ Scribed by C.E. Wulfman; R.D. Levine

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 386 KB
• Volume: 97
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(83)80508-9

✦ Synopsis

A general procedure for an algebraic formulation of the eigenvalue problem for hamiltonians which have both a discrete and a continuum spectrum is introduced. The onedimensional hiorse potential is used as an example, but more comples types of spectra can also be handled.

1 _ Introduction

The need for an algebraic description of the continuum states of anharmonic potentials arose, for us, in the context ofan algebraic treatment of multiphoton dissociation of diatomic molecules [ 11. Earlier studies (see ref. [2] for a summary) of the algebraic approach for anharmonic potentials have centered attention on the bound, discrete part of the spectrum. The present results demonstrate that the algebraic approach is