Closed Form Solutions For The Quantum LRS Bianchi IX and VIII Wheeler DeWitt Equations For An Arbitrary Hartle-Hawking Ordering Parameter

Abstract

In this paper we present the quantum LRS Bianchi IX models or, as they may be better known, the Taub-NUT models in addition to the quantum LRS Bianchi VIII models, both coupled to a stiff matter source. We solve their Wheeler DeWitt equations for an arbitrary Hartle-Hawking ordering parameter using separation of variables. Afterwards we construct a superposition of their respective wave functions and discuss some of the interesting qualitative properties they possess.