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Singularities of solutions of some Schrödinger equations on ${\text{R}}^n $
Author(s):
Alan
Weinstein;
Steven
Zelditch
Journal:
Bull. Amer. Math. Soc.
6
(1982),
449-452.
MSC (1980):
Primary 35S10;
Secondary 81C05
MathSciNet review:
648532
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References:
- 1.
- F. A. Berezin and M. A. Shubin, Symbols of operators and quantization, Colloq. Math. Soc. (Ja'nos Bolyai, ed., 5, Hilbert Space Operators, Tihany, Hungary, 1970), North-Holland, Amsterdam, London, 1972. MR 366281
- 2.
- R. P. Feynman and A. R. Hibbs, Quantum mechanics and path integrals, McGraw-Hill, New York, 1965.
- 3.
- G. B. Folland, Introduction to partial differential equations, Princeton Univ. Press, Princeton, N. J., 1976. MR 599578
- 4.
- A. Grossman, G. Loupias and E. M. Stein, An algebra of pseudo-differential operators and quantum mechanics in phase space, Ann. Inst. Fourier (Grenoble 18 (1968), 343—368.
- 5.
- V. Guillemin and S. Sternberg, The metaplectic representation, Weyl operators, and spectral theory, J. Funct. Anal. 42 (1981), 128-225. MR 624366
- 6.
- J. M. Souriau, Construction explicite de l'indice de Maslov, Applications, Lecture Notes in Math., vol. 570, Springer-Verlag, Berlin and New York, 1977, pp. 76-96. MR 471513
- 7.
- A. Voros, Asymptotic ħ-expansions of stationary quantum states, Ann. Inst. H. Poincaré Sect 26 A (N. S.) 26 (1977), 343-403. MR 456138
- 8.
- A. Weinstein, A symbol class for some Schrödinger equations on R , Amer. J. Math, (to appear). MR 778086
- 9.
- S. Zelditch, Reconstruction of singularities for solutions of Schrödinger equations, Ph.D. Thesis, Univ. of California, Berkeley, 1981.
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Additional Information:
DOI:
10.1090/S0273-0979-1982-15012-1
PII:
S 0273-0979(1982)15012-1
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