Lie Algebraic Solution of Linear Differential Equations

James Wei; Edward Norman

doi:10.1063/1.1703993

journal article Apr 01, 1963

Lie Algebraic Solution of Linear Differential Equations

James Wei Edward Norman

Journal of Mathematical Physics Vol. 4 No. 4 pp. 575-581 · AIP Publishing

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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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571

Citations

23

References

Details

Published: Apr 01, 1963
Vol/Issue: 4(4)
Pages: 575-581

Authors

J

James Wei

Socony Mobil Oil Company, Inc., Research Department, Paulsboro, New Jersey

E

Edward Norman

Socony Mobil Oil Company, Inc., Research Department, Paulsboro, New Jersey

Cite This Article

James Wei, Edward Norman (1963). Lie Algebraic Solution of Linear Differential Equations. Journal of Mathematical Physics, 4(4), 575-581. https://doi.org/10.1063/1.1703993

Lie Algebraic Solution of Linear Differential Equations

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