Equivalence between dynamical averaging methods of the Schrödinger equation: average Hamiltonian, secular averaging, and Van Vleck transformation

✍ Scribed by A. Llor

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 737 KB
• Volume: 199
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(92)80136-y

✦ Synopsis

To solve the Schri+dinger equation with a timedependent Hamiltonian, two main perturbation-expansion schemes arc available: secular averaging theory (SAT) and average Hamiltonian theory (AHT). Due to the lack ofan explicit relationship between SAT and AHT, some discrepancies between the results yielded by these theories have been found, especially in NMR applications. A general equivalence scheme between these two methods is here given in operator form, using a new formulation of SAT in terms of a static diagonalization expansion. The two approaches arc thus reconciled and the relationship with static techniques should eventually provide new and simpler convergence criteria for AHT.