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Book Review

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Book Information:

Author: Shmuel Agmon
Title: Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of $N$-body Schrödinger operators
Additional book information: Mathematical Notes, Vol. 29, Princeton University Press, Princeton, New Jersey, 1982, 118 pp., $10.50. ISBN 0-6910-8318-5.

References [Enhancements On Off] (What's this?)

  • 1. S. Agmon, On exponential decay of solutions of second order elliptic equations in unbounded domains, Proc. A. Pleijel Conf., Uppsala, September 1979, 1-18.
  • 2. S. Agmon, How do eigenfunctions decay? The case of N-body quantum systems (Proc. Sixth Internat. Conf. Math. Phys., Berlin, 1981), Lecture Notes in Physics, Springer-Verlag, 1982.
  • 3. Shmuel Agmon, Bounds on exponential decay of eigenfunctions of Schrödinger operators, Schrödinger operators (Como, 1984) Lecture Notes in Math., vol. 1159, Springer, Berlin, 1985, pp. 1–38. MR 824986, https://doi.org/10.1007/BFb0080331
  • 4. R. Alrichs, M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, "Schrödinger inequalities" and asymptotic behaviour of many electron densities, Phys. Rev. 16A (1977), 1782-1785.
  • 5. R. Alrichs, Bounds for the long range behaviour of electronic wave functions, J. Chem. Phys. 68 (1978), 1402-1410.
  • 6. René Carmona, Pointwise bounds for Schrödinger eigenstates, Comm. Math. Phys. 62 (1978), no. 2, 97–106. MR 505706
  • 7. R. Carmona and B. Simon, Pointwise bounds on eigenfunctions and wave packets in 𝑁-body quantum systems. V. Lower bounds and path integrals, Comm. Math. Phys. 80 (1981), no. 1, 59–98. MR 623152
  • 8. J. M. Combes and L. Thomas, Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators, Comm. Math. Phys. 34 (1973), 251-270. MR 391792
  • 9. P. Deift, W. Hunziker, B. Simon, and E. Vock, Pointwise bounds on eigenfunctions and wave packets in 𝑁-body quantum systems. IV, Comm. Math. Phys. 64 (1978/79), no. 1, 1–34. MR 516993
  • 10. T. Hoffmann-Ostenhof, A lower bound to the decay of ground states of two electron atoms, Phys. Lett. 77A (1980), 140-142.
  • 11. P. D. Lax, A Phragmen-Lindelöf theorem in harmonic analysis and its application to some questions in the theory of elliptic equations, Comm. Pure Appl. Math. 10 (1957), 361-389. MR 93706
  • 12. J. Morgan, III, The exponential decay of sub-continuum wave functions of two-electron atoms, J. Phys. A 10 (1977), L91-L93.
  • 13. T. O'Connor, Exponential decay of bound state wave functions, Comm. Math. Phys. 32 (1973), 319-340. MR 336119
  • 14. M. Reed and B. Simon, Methods of mathematical physics. Vol. 4: Analysis of operators, Academic Press, New York, 1978. MR 493421
  • 15. B. Simon, Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. I, Proc. Amer. Math. Soc. 42 (1974), 393-401. MR 417596
  • 16. Barry Simon, Instantons, double wells and large deviations, Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 2, 323–326. MR 684899, https://doi.org/10.1090/S0273-0979-1983-15104-2
  • 17. Barry Simon, Semiclassical analysis of low lying eigenvalues. II. Tunneling, Ann. of Math. (2) 120 (1984), no. 1, 89–118. MR 750717, https://doi.org/10.2307/2007072
  • 18. B. Helffer and J. Sjöstrand, Multiple wells in the semiclassical limit. I, Comm. Partial Differential Equations 9 (1984), no. 4, 337–408. MR 740094, https://doi.org/10.1080/03605308408820335

Review Information:

Reviewer: Percy Deift
Journal: Bull. Amer. Math. Soc. 12 (1985), 165-169
DOI: https://doi.org/10.1090/S0273-0979-1985-15332-7
American Mathematical Society