Quantum mechanics and statistical methods

Louis Fishman

Inge Svein Helland

The Basic Elements Statistical Theory and Practice Statistical Inference Under Symmetry The Transition from Statistics to Quantum Theory Quantum Mechanics from a Statistical Basis Further Development of Quantum Mechanics Decisions in Statistics Multivariate Data Analysis and Statistics Quantum Mechanics and the Diversity of Concepts.

Ryogo Kubo, Morikazu Toda, Natsuki Hashitsume

M. P. Nightingale, Cyrus J. Umrigar

In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the underlying mathematics is quite similar in that they are stochastic implementations of the power method. In all cases, optimized trial states can be used to reduce the errors of Monte Carlo estimates.

R. Shankar