论文信息 - On the Exponential Form of Time‐Displacement Operators in Quantum Mechanics

On the Exponential Form of Time‐Displacement Operators in Quantum Mechanics

We derive and discuss a formula, due to Magnus, for the exponential representation of the operator solution to Schrodinger's equation when the Hamiltonian is time dependent. The formula gives a unitary time‐displacement operator in every order of approximation. We study the usefulness of the first‐ and second‐order approximations for the kind of problem posed by the semiclassical theory of inelastic collisions, basing our discussion on two exactly soluble two‐state problems. The algebraic structure of the Magnus formula is in itself useful; to illustrate this, we solve exactly the problems of the linearly forced harmonic oscillator and the harmonic oscillator with time‐dependent force constant.

John C. Light | J. Light | P. Pechukas | Philip Pechukas

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