Cyclic Operator Decomposition for Solving the Differential Equations

Ivan Gonoskov^{*}

Show more

References

[1] F. J. Dyson, “Divergence of Perturbation Theory in Quantum Electrodynamics,” Physical Review, Vol. 85, No. 4, 1952, pp. 631-632. doi:10.1103/PhysRev.85.631

[2] A. V. Turbiner, “The Eigenvalue Spectrum in Quantum Mechanics and the Nonlinearization Procedure,” Soviet Physics Uspekhi, Vol. 27, No. 9, 1984, p. 668.
doi:10.1070/PU1984v027n09ABEH004155

[3] J. Fleck, J. Morris and M. Feit, “Time-Dependent Propagation of High Energy Laser Beams through the Atmosphere,” Applied Physics A: Materials Science and Processing, Vol. 10, No. 2, 1976, pp. 129-160.
doi:10.1007/BF00896333

[4] A. N. Drozdov and S. Hayashi, “Numerical Test of Approximate Single-Step Propagators: Harmonic Power Series Expansions versus System-Specific Split Operator Representations,” Physical Review E, Vol. 59, No. 2, 1999, pp. 1386-1397. doi:10.1103/PhysRevE.59.1386

[5] J. V. Corbett and J. Math, “Convergence of the Born Se- ries,” Journal of Mathematical Physics, Vol. 9, No. 6, 1968, p. 891. doi:10.1063/1.1664655

[6] M. Wellner, “Improvement of the Born Series at Low Energy,” Physical Review, Vol. 132, No. 4, 1963, pp. 1848-1853. doi:10.1103/PhysRev.132.1848

[7] R. Perez and J. Math, “On the Expansion of the Propagator in Power Series of the Coupling Constant,” Journal of Mathematical Physics, Vol. 20, No. 2, 1979, p. 241.
doi:10.1063/1.524070

[8] F. S. Bemfica and H. O. Girotti, “Born Series and Unitarity in Noncommutative Quantum Mechanicsphys,” Physical Review D, Vol. 77, No. 2, 2008, Article ID: 027704. doi:10.1103/PhysRevD.77.027704

[9] F. J. Dyson, “The S Matrix in Quantum Electrodynamics,” Physical Review, Vol. 75, No. 11, 1949, pp. 1736- 1755. doi:10.1103/PhysRev.75.1736

[10] J. H. Eberly and H. R. Reiss, “Electron Self-Energy in Intense Plane-Wave Field,” Physical Review, Vol. 145, No. 4, 1966, pp. 1035-1040. doi:10.1103/PhysRev.145.1035

[11] H. R. Reiss and J. H. Eberly, “Green’s Function in Intense-Field Electrodynamics,” Physical Review, Vol. 151, No. 4, 1966, pp. 1058-1066.
doi:10.1103/PhysRev.151.1058

[12] A. Mockel and J. Math, “Invariant Imbedding as a Generalization of the Resolvent Equation,” Journal of Mathematical Physics, Vol. 8, No. 12, 1967, p. 2318.
doi:10.1063/1.1705158

[13] B. Curgus and T. T. Read, “Discreteness of the Spectrum of Second-Order Differential Operators and Associated Embedding Theorems,” Journal of Differential Equations, Vol. 184, No. 2, 2002, pp. 526-548.
doi:10.1006/jdeq.2001.4152

[14] L. Landau and E. Lifshitz, “Quantum Mechanics Non-Relativistic Theory,” 3rd Edition, Pergamon Press, Oxford, 1977.

[15] L. Schiff, “Quantum Mechanics,” 3rd Edition, McGraw Hill, New York, 1968.

[16] F. J. Dyson, “The Schrodinger Equation in Quantum Electrodynamics,” Physical Review, Vol. 83, No. 6, 1951, pp. 1207-1216.

[17] L. Landau and E. Lifshitz, “Electrodynamics of Continuous Media,” Vol. 8, Butterworth-Heinemann, Oxford, 1984.