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Convergence of the Magnus expansion

1990; American Physical Society; Volume: 41; Issue: 5 Linguagem: Inglês

10.1103/physreva.41.2311

1538-4446

Francisco M. Fernández,

Quantum Information and Cryptography

The convergence of the Magnus expansion in the Schr\"odinger representation is investigated with the aid of two exactly solvable models. A baffling observation regarding the dynamics of a spin-(1/2 system driven by a superposition of a constant and a rotating magnetic field is elucidated. Perturbation theory is applied to the exponential solution to the Schr\"odinger equation for a time-dependent harmonic oscillator. The first terms of the perturbation expansion for the singularity of the exponent are exactly calculated. The scope and limitations of perturbation theory in obtaining the range of validity of the Magnus expansion are discussed.