What question did this study set out to answer?

To develop an exact and tractable mathematical framework for solving the Schrödinger equation in quantum systems driven by time-periodic oscillating fields.

May 24, 1965Physical Review

Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time

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Authors

JSJ.H. ShirleyCalifornia Institute of Technology

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Implication

Theoretical analysis demonstrates an infinite-matrix Hamiltonian framework for quantum systems in periodic fields, suggesting simpler calculation of multi-quantum resonance transitions.

Key Points

To develop an exact and tractable mathematical framework for solving the Schrödinger equation in quantum systems driven by time-periodic oscillating fields.
Transformed the semiclassical time-dependent Hamiltonian into an equivalent time-independent Hamiltonian expressed as an infinite matrix.
Combined the infinite-matrix formulation with perturbation theory for two nearly degenerate states.
Evaluated the formalism using a model of a two-state quantum system perturbed by a strong oscillating field.
Established a time-independent eigenvalue problem mathematically equivalent to the time-dependent semiclassical treatment and interpretable as a classical field approximation.
Derived analytical expressions for resonance transition probabilities, multi-quantum transitions, and frequency shifts under strong field conditions.

Cite This Study

J.H. Shirley (1965) studied this question.

synapsesocial.com/papers/69dc2fb54f901957bec0fabe https://doi.org/10.1103/physrev.138.b979

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Implication

Theoretical analysis demonstrates an infinite-matrix Hamiltonian framework for quantum systems in periodic fields, suggesting simpler calculation of multi-quantum resonance transitions.

Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time

Discussion

Member takes

Implication

Key Points

Cite This Study

Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time

Discussion

Member takes

Implication

Key Points

Cite This Study

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