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Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems IV

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Abstract

We describe several new techniques for obtaining detailed information on the exponential falloff of discrete eigenfunctions ofN-body Schrödinger operators. An example of a new result is the bound (conjectured by Morgan)\(\left| {\psi (x_1 \ldots x_N )} \right| \leqq C\exp ( - \sum\limits_1^N {\alpha _n r_n )}\) for an eigenfunction ω of

$$H_N = - \sum\limits_{i = 1}^N {(\Delta _i - } \left. {\frac{Z}{{\left| {x_i } \right|}}} \right) + \sum\limits_{i< j} {\left| {x_i - x_j } \right|^{ - 1} }$$

with energyE N . In this boundr 1 r 2...r N are the radii |x i | in increasing order and the α's are restricted by α n <(E n−1−E n )1/2, whereE n , forn=0, 1,...,N−1, is the lowest energy of the system described byH n . Our methods include subharmonic comparison theorems and “geometric spectral analysis”.

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Authors and Affiliations

  1. Courant Institute, NYU, New York, USA

    P. Deift

  2. Institut für Theoretische Physik, ETH Zïch, CH-8093, Zürich, Switzerland

    W. Hunziker & E. Vock

  3. Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey, USA

    B. Simon

Authors
  1. P. Deift
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  2. W. Hunziker
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  3. B. Simon
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  4. E. Vock
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Additional information

Communicated by J. Glimm

Research supported in part by grants from the USNSF

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Deift, P., Hunziker, W., Simon, B. et al. Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems IV. Commun.Math. Phys. 64, 1–34 (1978). https://doi.org/10.1007/BF01940758

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