Bulletin of the American Mathematical Society

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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.

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.

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, DOI 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.

René Carmona, Pointwise bounds for Schrödinger eigenstates, Comm. Math. Phys. 62 (1978), no. 2, 97–106. MR 505706

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

J. M. Combes and L. Thomas, Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators, Comm. Math. Phys. 34 (1973), 251–270. MR 391792

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.

P. D. Lax, 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.

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

A. J. O’Connor, Exponential decay of bound state wave functions, Comm. Math. Phys. 32 (1973), 319–340. MR 336119

Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419

Barry Simon, 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

Barry Simon, 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

Barry Simon, Semiclassical analysis of low lying eigenvalues. II. Tunneling, Ann. of Math. (2) 120 (1984), no. 1, 89–118. MR 750717, DOI 10.2307/2007072

B. Helffer and J. Sjöstrand, Multiple wells in the semiclassical limit. I, Comm. Partial Differential Equations 9 (1984), no. 4, 337–408. MR 740094, DOI 10.1080/03605308408820335

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.

S. Agmon, Bounds on exponential decay of eigenfunctions of Schrödinger operators, C. I. M. E. lectures, Como, 1984 (preprint). MR 0824986

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.

R. Carmona, Pointwise bounds for Schrödinger eigenstates, Comm. Math. Phys. 62 (1978), 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), 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), 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.

B. Simon, Instantons, double wells and large deviations, Bull. Amer. Math. Soc. 9 (1983), 323-326. MR 684899

17.

B. Simon, Semiclassical analysis of low lying eigenvalues, II. Tunnelling, Ann. Math. (to appear). MR 750717

18.

J. Sjöstrand and B. Helffer, Multiple wells in the semiclassical limit. I, Comm. Partial Differential Equations (to appear). MR 740094