Book Review
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MathSciNet review:
1567202
Full text of review:
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Book Information:
Author:
Willard Miller Jr.
Title:
Symmetry and separation of variables
Additional book information:
Addison-Wesley Publishing Company, Reading, Massachusetts, 1977, xxx + 285 pp., $21.50.
1. M. Bôcher, Die Reihenentwickelungen der Potentialtheorie, Leipzig, 1894.
Luther Pfahler Eisenhart, Separable systems of Stackel, Ann. of Math. (2) 35 (1934), no. 2, 284–305. MR 1503163, DOI 10.2307/1968433
Peter Havas, Separation of variables in the Hamilton-Jacobi, Schrödinger, and related equations. I. Complete separation, J. Mathematical Phys. 16 (1975), 1461–1468. MR 403463, DOI 10.1063/1.522694
E. G. Kalnins and W. Miller Jr., Lie theory and the wave equation in space-time. I. The Lorentz group, J. Mathematical Phys. 18 (1977), no. 1, 1–16. MR 507308, DOI 10.1063/1.523130
5. W. Miller, J. Patera and P. Winternitz, Subgroups of Lie groups and separation of variables. Report CRM-813, Centre de Recherches Mathématiques, Université de Montréal, 1978.
Parry Moon and Domina Eberle Spencer, Field theory handbook. Including coordinate systems, differential equations and their solution, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0136092
Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
Heinz-Dieter Niessen, Algebraische Untersuchungen über separierbare Operatoren, Math. Z. 94 (1966), 328–348 (German). MR 211055, DOI 10.1007/BF01111665
M. N. Olevskiĭ, Triorthogonal systems in spaces of constant curvature in which the equation $\Delta _2u+\lambda u=0$ allows a complete separation of variables, Mat. Sbornik N.S. 27(69) (1950), 379–426 (Russian). MR 0038535
H. P. Robertson, Bemerkung über separierbare Systeme in der Wellenmechanik, Math. Ann. 98 (1928), no. 1, 749–752 (German). MR 1512435, DOI 10.1007/BF01451624
11. P. Stäckel, Über die Integration der Hamilton-Jacobischen Differentialgleichung mittels Separation der Variabelen, Habilitationsschrift, Halle, 1891.
P. Winternitz and I. Friš, Invariant expansions of relativistic amplitudes and subgroups of the proper Lorentz group, Soviet J. Nuclear Phys. 1 (1965), 636–643. MR 0202919
E. G. Kalnins and Willard Miller Jr., Killing tensors and variable separation for Hamilton-Jacobi and Helmholtz equations, SIAM J. Math. Anal. 11 (1980), no. 6, 1011–1026. MR 595827, DOI 10.1137/0511089
- 1.
- M. Bôcher, Die Reihenentwickelungen der Potentialtheorie, Leipzig, 1894.
- 2.
- L. P. Eisenhart, Separable systems of Stäckel, Ann. of Math. 35 (1934), 284-305. MR 1503163
- 3.
- P. Havas, Separation of variables in the Hamilton-Jacobi, Schrödinger and related equations, 1. Complete separation, J. Mathematical Phys. 16 (1975), 1461-1468. MR 403463
- 4.
- E. G. Kalnins and W. Miller, Lie theory and the wave equation in space-time. 5. R-separable solutions of the wave equation, J. Mathematical Phys. 19 (1978), 1247-1257. MR 507313
- 5.
- W. Miller, J. Patera and P. Winternitz, Subgroups of Lie groups and separation of variables. Report CRM-813, Centre de Recherches Mathématiques, Université de Montréal, 1978.
- 6.
- P. Moon and D. E. Spencer, Field theory handbook, Springer-Verlag, Berlin, 1961. MR 136092
- 7.
- Ph. M. Morse and H. Feshbach, Methods of theoretical physics. Part I, McGraw-Hill, New York, 1953. MR 59774
- 8.
- H.-D. Niessen, Algebraische Untersuchungen über separierbare Operatoren, Math. Z. 94 (1966), 328-348. MR 211055
- 9.
- P. Olevski, The separation of variables in the equation ∆, Mat. Sb. 27 (69) (1950), 379-426. (Russian) MR 38535
- 10.
- H. P. Robertson, Bemerkung über separierbare Systeme in der Wellenmechanik, Math. Ann. 98 (1928), 749-752. MR 1512435
- 11.
- P. Stäckel, Über die Integration der Hamilton-Jacobischen Differentialgleichung mittels Separation der Variabelen, Habilitationsschrift, Halle, 1891.
- 12.
- P. Winternitz and I. Fris, Invariant expansions of relativistic amplitudes and subgroups of the proper Lorentz group, Soviet Physics JNP 1 (1965), 636-643. MR 202919
- 13.
- E. G. Kalnins and W. Miller, Killing tensors and variable separation for Hamilton-Jacobi and Helmholtz equations (preprint). MR 595827
Review Information:
Reviewer:
Tom H. Koornwinder
Journal:
Bull. Amer. Math. Soc.
1 (1979), 1014-1019
DOI:
https://doi.org/10.1090/S0273-0979-1979-14723-2
