High-order stark effect perturbation series for hydrogenic ions via the perturbational-variational Rayleigh-Ritz formalism

✍ Scribed by Jeremiah N. Silverman; Jürgen Hinze

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 950 KB
• Volume: 128
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(86)80655-8

✦ Synopsis

Perturbation theory combined with the variational principle in the form of the perturbational-variational

Rayleigh-Ritz (PV RR) matrix formalism is a powerful method for applying large-order perturbation theory to the Stark effect for hydrogenic ions. A paradigm is derived and implemented which permits the precise construction of a variational ansatz from which the Stark Rayleigh-Schrodinger (RS) eigenvahte (pqlarizability) and eigenfunction perturbation series for the ground state are generated via PV RR to any prespecified order. We have also computed high-order RS series of the kinetic-and potential-energy components of the Stark eigenvalue series, and determined the Bender-Wu-type asymptotic formulae which govern the limiting behaviour of their large-order coefficients. PV RR is not restricted to one-electron systems.