Book Review

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MathSciNet review: 1567535

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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.

**1.**

*On exponential decay of solutions of second order elliptic equations in unbounded domains*, Proc. A. Pleijel Conf., Uppsala, September 1979, 1-18.

**2.**

*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.

*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**, DOI 10.1007/BFb0080331

**4.**

*Schrödinger inequalities*"

*and asymptotic behaviour of many electron densities*, Phys. Rev. 16A (1977), 1782-1785.

**5.**

*Bounds for the long range behaviour of electronic wave functions*, J. Chem. Phys. 68 (1978), 1402-1410.

*Pointwise bounds for Schrödinger eigenstates*, Comm. Math. Phys.

**62**(1978), no. 2, 97–106. MR

**505706**

*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**

*Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators*, Comm. Math. Phys.

**34**(1973), 251–270. MR

**391792**

*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.**

*A lower bound to the decay of ground states of two electron atoms*, Phys. Lett. 77A (1980), 140-142.

*A Phragmén-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**, DOI 10.1002/cpa.3160100305

**12.**

*The exponential decay of sub-continuum wave functions of two-electron atoms*, J. Phys. A 10 (1977), L91-L93.

*Exponential decay of bound state wave functions*, Comm. Math. Phys.

**32**(1973), 319–340. MR

**336119**

*Methods of modern mathematical physics. I. Functional analysis*, Academic Press, New York-London, 1972. MR

**0493419**

*Pointwise bounds on eigenfunctions and wave packets in $N$-body quantum systems. I, II*, Proc. Amer. Math. Soc.

**42**(1974), 395–401: ibid. 45 (1974), 454–456. MR

**417596**, DOI 10.1090/S0002-9939-1974-0417596-0

*Instantons, double wells and large deviations*, Bull. Amer. Math. Soc. (N.S.)

**8**(1983), no. 2, 323–326. MR

**684899**, DOI 10.1090/S0273-0979-1983-15104-2

*Semiclassical analysis of low lying eigenvalues. II. Tunneling*, Ann. of Math. (2)

**120**(1984), no. 1, 89–118. MR

**750717**, DOI 10.2307/2007072

*Multiple wells in the semiclassical limit. I*, Comm. Partial Differential Equations

**9**(1984), no. 4, 337–408. MR

**740094**, DOI 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