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

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

doi:10.1007/BF01940758

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We describe several new techniques for obtaining detailed information on the exponential falloff of discrete eigenfunctions of N-body Schrödinger operators. An example of a new result is the bound (conjectured by Morgan) {Mathematical expression} for an eigenfunction ω of {Mathematical expression} with energy E_N. In this bound r₁r₂... 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, where E_n, for n=0, 1,..., N-1, is the lowest energy of the system described by H_n. Our methods include subharmonic comparison theorems and "geometric spectral analysis".

Original language	English (US)
Pages (from-to)	1-34
Number of pages	34
Journal	Communications In Mathematical Physics
Volume	64
Issue number	1
DOIs	https://doi.org/10.1007/BF01940758
State	Published - Dec 1978

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems IV",

abstract = "We describe several new techniques for obtaining detailed information on the exponential falloff of discrete eigenfunctions of N-body Schr{\"o}dinger operators. An example of a new result is the bound (conjectured by Morgan) {Mathematical expression} for an eigenfunction ω of {Mathematical expression} with energy EN. In this bound r1r2... rN are the radii |xi| in increasing order and the α's are restricted by αn<(En-1-En)1/2, where En, for n=0, 1,..., N-1, is the lowest energy of the system described by Hn. Our methods include subharmonic comparison theorems and {"}geometric spectral analysis{"}.",

author = "P. Deift and W. Hunziker and B. Simon and E. Vock",

year = "1978",

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AB - We describe several new techniques for obtaining detailed information on the exponential falloff of discrete eigenfunctions of N-body Schrödinger operators. An example of a new result is the bound (conjectured by Morgan) {Mathematical expression} for an eigenfunction ω of {Mathematical expression} with energy EN. In this bound r1r2... rN are the radii |xi| in increasing order and the α's are restricted by αn<(En-1-En)1/2, where En, for n=0, 1,..., N-1, is the lowest energy of the system described by Hn. Our methods include subharmonic comparison theorems and "geometric spectral analysis".

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

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