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Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
Abstract
The interaction of a quantum system with an oscillating field is studied in a formalism which replaces the semiclassical time-dependent Hamiltonian with a time-independent Hamiltonian represented by an infinite matrix. The formalism is developed as a mathematical equivalent to the semiclassical treatment, and interpreted as a classical approximation to the quantum treatment of the field. Combined with a perturbation theory for two nearly degenerate states, the formalism provides a convenient method for determining resonance transition probabilities including frequency shifts and multiple quantum transitions. The theory is illustrated by a detailed study of the simple case of a two-state system excited by a strong oscillating field.
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Cited by
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Topological characterization of periodically driven quantum systems
Kitagawa, T., Berg, E., Rudner, M., & Demler, E. (2010) · Physical Review B · doi:10.1103/physrevb.82.235114 · Cited by 1,239
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Eckardt, A. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.011004 · Cited by 1,207
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Metadata
- Authors
- Shirley, J. H.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1965-05-24
- Volume
- 138
- Issue
- 4B
- Pages
- B979-B987
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2004871937
- Cited by
- 2,887
- References
- 0
- FWCI
- 0.98
- Type
- journal article
- Language
- en
- Open access
- closed
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- Shirley, J. H. (1965). Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time. Physical Review. https://doi.org/10.1103/physrev.138.b979
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