Open Access
October, 1999 Quantum ergodicity at a finite energy level
Tatsuya Tate
J. Math. Soc. Japan 51(4): 867-885 (October, 1999). DOI: 10.2969/jmsj/05140867


The purpose of this paper is to formulate the notion of quantum ergodicity at a finite energy level for certain quantum mechanics, by using the method of Sunada [Sul]. Under some assumptions on the corresponding classical mechanics, we obtain a necessary and sufficient condition in terms of semi-classical asymptotic behaviour of eigenfunctions of a quantum Hamiltonian so that the classical mechanics is ergodic. We also obtain a result on quantum weak mixing at a finite energy level which is a semiclassical analogue of the notion introduced in [Z4].


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Tatsuya Tate. "Quantum ergodicity at a finite energy level." J. Math. Soc. Japan 51 (4) 867 - 885, October, 1999.


Published: October, 1999
First available in Project Euclid: 10 June 2008

zbMATH: 0948.37052
MathSciNet: MR1705252
Digital Object Identifier: 10.2969/jmsj/05140867

Primary: 58G25 , 81Q50

Keywords: quantum ergodicity , reduction , semi-classical limit

Rights: Copyright © 1999 Mathematical Society of Japan

Vol.51 • No. 4 • October, 1999
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