Generalized Adiabatic Product Expansion: A nonperturbative method of solving time-dependent Schroedinger equation

Abstract

We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a finite number of terms, and our method gives the exact solution of the corresponding time-dependent Schroedinger equation. We apply this method to study the dynamics of a general nondegenerate two-level quantum system, a time-dependent classical harmonic oscillator, and a degenerate system consisting of a spin 1 particle interacting with a time-dependent electric field E(t) through the Stark Hamiltonian H=λ[J.E(t)]^2.

19 pages, accepted for publication in J. Math. Phys

References in corpus (2)

• Time-Dependent Diffeomorphisms as Quantum Canonical Transformations and the Time-Dependent Harmonic Oscillator
• The SU(2) instanton and the adiabatic evolution of two Kramers doublets

Cited by in corpus (8)

• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Shortcuts to adiabaticity for non-Hermitian systems
• Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Linear Pseudo-fermions
• Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
• Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
• Adiabatic Series Expansion and Higher-Order Semiclassical Approximations in Scattering Theory