β Scribed by J.P. Gazeau; J. Renaud
No coin nor oath required. For personal study only.
First we give a detailed description of the contraction of an (S U(1,1)) elementary system to its "Newtonian" limit, i.e., the harmonic oscillator. In this context we derive a star-product formula for this system and prove a theorem of continuity for this product with respect to the contraction. Then we consider the Lie algorithm for a perturbation of the (S U(1,1)) free Hamiltonian. The classical case and the quantum case are solved. The classical version is the classical limit ((h \rightarrow 0)) of the quantum one and we calculate explicitly all the quantum corrections. Moreover the contraction ((c \rightarrow \infty)) gives the Newtonian version of the algorithm. We also show that the quantum energy levels can be obtained via a Bohr Sommerfeld formula. ic 1993 Academic Press. Inc.
π SIMILAR VOLUMES
An Intelligent Fixturing System (IFS) is currently being developed to hold a family of cylinder heads for machining operations. This system incorporates a Part Location System (PLS) to locate the workpiece reference frame of a cylinder head relative to a pallet. This two-part paper describes the dev