Communications in Mathematical Physics

, Volume 64, Issue 1, pp 1–34 | Cite as

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

  • P. Deift
  • W. Hunziker
  • B. Simon
  • E. Vock


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 boundr1r2...r N are the radii |x i | in increasing order and the α's are restricted by α n <(En−1E 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”.


Neural Network Statistical Physic Lower Energy Complex System Spectral Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • P. Deift
    • 1
  • W. Hunziker
    • 2
  • B. Simon
    • 3
  • E. Vock
    • 2
  1. 1.Courant InstituteNYUNew YorkUSA
  2. 2.Institut für Theoretische PhysikETH ZïchZürichSwitzerland
  3. 3.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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