The University of Queensland
Department of Mathematics
Mathematical Physics Seminar
Kahler Manifolds & Quantum Mechanics
Dr D S McAnally
Department of Mathematics and statistics
Wednesday, 19th July, 2.00pm
67-111 Priestley Building
The inner product on the Hilbert space for an n-state quantum mechanical system (along with its complex structure) induces the structure of a Kahler manifold on the space of quantum mechanical states, CP^{n-1}. The simple relationship between the Hamiltonian function on the Kahler manifold (treated as a symplectic manifold) and the Hamiltonian operator on the Hilbert space are discussed. The importance of the expectation value of a hermitian operator is also discussed, and the uncertainty of a hermitian operator is given a geometric interpretation on the Kahler manifold, which will lead to the manifestation of Heisenberg Uncertainty Relations as geometric statements on the manifold.
All interested are invited to attend.
Enquires to Yao-Zhong Zhang on 3365 2309 or yzz@maths.uq.edu.au