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Pointwise bounds on eigenfunctions and wave packets in $ N$-body quantum systems. I

Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 42 (1974), 395-401
MSC: Primary 35P99; Secondary 81.47
Part II: Proc. Amer. Math. Soc. 45, no. 3 (1974), 454-456
MathSciNet review: 0417596
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Abstract: We provide a simple proof of (a modification of) Kato's theorem on the Hölder continuity of wave packets in N-body quantum systems. Using this method of proof and recent results of O'Connor, we prove a pointwise bound

$\displaystyle \vert\Psi (\zeta )\vert \leqq {D_\varepsilon }\exp [ - (1 - \varepsilon ){a_0}\vert x\vert]$

on discrete eigenfunctions of energy E. Here $ \varepsilon > 0,a_0^2 = 2$ (mass of the system) $ [{\text{dist}}(E,{\sigma _{{\text{ess}}}})]$ and $ \vert x\vert$ is the radius of gyration.

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

  • [1] R. Ahlrichs, Asymptotic behavior of atomic bound state wave functions, Univ. of Karlsruhe, April 1972 (preprint). MR 0363232 (50:15670)
  • [2] T. Kato, On the eigenfunctions of many-particle systems in quantum mechanics, Comm. Pure Appl. Math. 10 (1957), 151-177. MR 19, 501. MR 0088318 (19:501a)
  • [3] A. O'Connor, Thesis, Princeton University, Princeton, N.J., 1972.
  • [4] -, Exponential decay of bound state wave functions, Comm. Math. Phys. (to appear). MR 0336119 (49:895)
  • [5] B. Simon, Quantum mechanics for Hamiltonians defined as quadratic forms, Princeton Univ. Press, Princeton, N.J., 1971. MR 0455975 (56:14207)

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