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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Singularities of solutions of some Schrödinger equations on ${\text{R}}^n $


Authors: Alan Weinstein and Steven Zelditch
Journal: Bull. Amer. Math. Soc. 6 (1982), 449-452
MSC (1980): Primary 35S10; Secondary 81C05
MathSciNet review: 648532
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  • 1. F. A. Berezin and M. A. Šubin, Symbols of operators and quantization, Hilbert space operators and operator algebras (Proc. Internat. Conf., Tihany, 1970) North-Holland, Amsterdam, 1972, pp. 21–52. Colloq. Math. Soc. János Bolyai, No. 5. MR 0366281 (51 #2529)
  • 2. R. P. Feynman and A. R. Hibbs, Quantum mechanics and path integrals, McGraw-Hill, New York, 1965.
  • 3. Gerald B. Folland, Introduction to partial differential equations, Princeton University Press, Princeton, N.J., 1976. Preliminary informal notes of university courses and seminars in mathematics; Mathematical Notes. MR 0599578 (58 #29031)
  • 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), no. 2, 128–225. MR 624366 (83i:58101), http://dx.doi.org/10.1016/0022-1236(81)90042-2
  • 6. Jean-Marie Souriau, Interprétation géométrique des états quantiques, Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975) Springer, Berlin, 1977, pp. 76–96. Lecture Notes in Math., Vol. 570 (French). MR 0471513 (57 #11243)
  • 7. A. Voros, Asymptotic \hbar-expansions of stationary quantum states, Ann. Inst. H. Poincaré Sect. A (N.S.) 26 (1977), no. 4, 343–403 (English, with French summary). MR 0456138 (56 #14366)
  • 8. Alan Weinstein, A symbol class for some Schrödinger equations on 𝑅ⁿ, Amer. J. Math. 107 (1985), no. 1, 1–21. MR 778086 (87a:58150), http://dx.doi.org/10.2307/2374454
  • 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: http://dx.doi.org/10.1090/S0273-0979-1982-15012-1
PII: S 0273-0979(1982)15012-1