A subject of interest in classical and quantum mechanics is the development of the appropriate treatment of the time variable. In this paper we introduce a method of choosing the initial time eigensurface and how this method can be used to generate time-energy coordinates and, consequently, time-energy representations for classical and quantum systems.

The ZX calculus is a diagrammatic language for quantum mechanics and quantum information processing. We prove that the ZX-calculus is not complete for the Clifford+T quantum mechanics. The completeness for this fragment has been stated as one of the main current open problems in categorical quantum mechanics [8]. The ZX calculus was known to be incomplete for quantum mechanics [7], on the other...

The statistical mechanics of systems whose evolution is governed by mixed quantum-classical dynamics is investigated. The algebraic properties of the quantum-classical time evolution of operators and of the density matrix are examined and compared to those of full quantum mechanics. The equilibrium density matrix that appears in this formulation is stationary under the dynamics and a method for...

The molecular electrostatic potential inside the potassium channel protein from Streptomyces liVidans has been investigated using linear scaling semiempirical quantum chemical method, for a variety of geometries, with and without solvating water molecules. The results are compared with those given by a number of popular molecular mechanics force-fields. The difference between the quantum and mo...

How do our ideas about quantum mechanics affect our understanding of spacetime? This familiar question leads to quantum gravity. This talk addressed a complementary question: How do our ideas about spacetime affect our understanding of quantum mechanics? Familiar non-relativistic quantum theory illustrates how quantum mechanics incorporates assumptions about spacetime. The Schrödinger equation ...