Browsing by Subject "Hilbert space"
Now showing 1 - 4 of 4
Results Per Page
Sort Options
Item Introduction to quantum probability(2011-08) Cui, Cong; Hadjicostas, Petros; Ruymgaart, FritsThis thesis is a review of the quantum logic approach to quantum probability theory which was first studied by Birkhoff and von Neumann in 1936. Our study is based on the more general quantum structure which is known as the $\sigma$-orthocomplete orthomodular poset or quantum logic. We introduce the definitions of states and observables and show that the quantum probability theory is a generalization of the classical probability theory due to Kolmogorov. Discussions about joint distributions of observables are given, and we also give the general expression of the uncertainty relation in the logico-algebraic sense which generalizes the well-known Heisenberg uncertainty relation. Two examples, the classical probability structure of Kolmogorov and the Hilbert space quantum logic, are given as illustrations throughout the whole discussion.Item On representing resonances and decaying states(2001-08) Harshman, Nathan Lee; Böhm, Arno, 1936-Item The projective representations of the extended Poincaré group and applications(2003) Scurek, Raymond Benjamin; Böhm, ArnoItem Random perturbation of a self-adjoint operator with a multiple eigenvalue(2012-05) Gaines, George; Ruymgaart, Frits; Gilliam, David S.; Trindade, A. AlexandreWe first consider a bounded self-adjoint operator on a Hilbert space with a multiple eigenvalue as its largest eigenvalue. We perturb the operator and study the resulting cluster of eigenvalues of the perturbed operator. We study the convergence of the scattered eigenvalues to the original. We then do computer simulations. We also show an approximation for Brownian motion.