Connections between perturbation theory and the Van Vleck transformation: Illustrative calculations on the perturbed harmonic oscillator

✍ Scribed by Paul Westhaus

• Publisher: John Wiley and Sons
• Year: 1982
• Tongue: English
• Weight: 578 KB
• Volume: 21
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560210309

✦ Synopsis

Abstract

We continue to examine the connection between perturbation theory and the Van Vleck unitary transformation. Here we illustrate the formalism derived earlier by applying it to compute the stationary states of the perturbed harmonic oscillator. We find that each solution of the traditional Brillouin‐Wigner perturbation theory equations gives rise to a different unitary transformation which, when operating on the unperturbed ground state, produces one or the other of the perturbed eigenstates. With any of the perturbed states able to be reached by a unitary transformation on the unperturbed ground state, we advise caution in using approximate solutions of the perturbation equations in general cases, lest an unexpected stationary state be obtained.