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Lie Algebraic Solution of Linear Differential Equations
Abstract
The solution U(t) to the linear differential equation dU/dt = h(t)U can be represented by a finite product of exponential operators; In many interesting cases the representation is global. U(t) = exp[g1(t)H1] exp [g2(t)H2] … exp[gn(t)Hn] where gi(t) are scalar functions and Hi are constant operators. The number, n, of terms in this expansion is equal to the dimension of the Lie algebra generated by H(t). Each term in this product has time-independent eigenvectors. Some applications of this solution to physical problems are given.
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Citations
Cited by
Exponential Operators and Parameter Differentiation in Quantum Physics
Wilcox, R. M. (1967) · Journal of Mathematical Physics · doi:10.1063/1.1705306 · Cited by 1,207
The Magnus expansion and some of its applications
Blanes, S., Casas, F., Oteo, J. A., & Ros, J. (2009) · Physics Reports · doi:10.1016/j.physrep.2008.11.001 · Cited by 1,157
Multiphoton quantum optics and quantum state engineering
Dell’Anno, F., De Siena, S., & Illuminati, F. (2006) · Physics Reports · doi:10.1016/j.physrep.2006.01.004 · Cited by 310
Multimode squeeze operators and squeezed states
Ma, X., & Rhodes, W. (1990) · Physical Review A · doi:10.1103/physreva.41.4625 · Cited by 150
Metadata
- Authors
- Wei, J., & Norman, E.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1963-04-01
- Volume
- 4
- Issue
- 4
- Pages
- 575-581
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2007171191
- Cited by
- 651
- References
- 0
- FWCI
- 1.80
- Type
- journal article
- Language
- en
- Open access
- closed
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