Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ N$-body Schrödinger operators with finitely many bound states


Authors: W. D. Evans and Roger T. Lewis
Journal: Trans. Amer. Math. Soc. 322 (1990), 593-626
MSC: Primary 35P15; Secondary 35J10, 47F05, 81U10
MathSciNet review: 974515
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider a class of second-order elliptic operators which includes atomic-type $ N$-body operators for $ N > 2$. Our concern is the problem of predicting the existence of only a finite number of bound states corresponding to eigenvalues below the essential spectrum. We obtain a criterion which is natural for the problem and easy to apply as is demonstrated with various examples. While the criterion applies to general second-order elliptic operators, sharp results are obtained when the Hamiltonian of an atom with an infinitely heavy nucleus of charge $ Z$ and $ N$ electrons of charge $ 1$ and mass $ \tfrac{1} {2}$ is considered.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35P15, 35J10, 47F05, 81U10

Retrieve articles in all journals with MSC: 35P15, 35J10, 47F05, 81U10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0974515-X
PII: S 0002-9947(1990)0974515-X
Article copyright: © Copyright 1990 American Mathematical Society