The Real Symplectic Groups in Quantum Mechanics and Optics

text of abstract (We present a utilitarian review of the family of matrix groups $Sp(2n,\Re)$, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of $Sp(2n,\Re)$. Global decomposition theorems, interesting subgroups and their generators are described. Turning to $n$-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under $Sp(2n,\Re)$ action are delineated.)Comment: Review article 43 pages, revtex, no figures, replaced because somefonts were giving problem in autometic ps generatio

TWO-SURFACE OPTICAL SYSTEMS WITH ZERO THIRD-ORDER SPHERICAL ABERRATION

QC 351 A7 no. 37This paper derives four one-parameter families of two-surface optical systems having the property that, relative to a well-defined pair of conjugate points, one finite and the other infinite, third-order spherical aberration is zero. The two surfaces can be either refracting or reflecting. Aperture planes are defined for which third-order astigmatism is zero. An expression for coma is also derived. Assuming that the systems will be constructible, a means of defining domains for the free parameter is indicated. Possible applications of these results to optical design are included.This title from the Optical Sciences Technical Reports collection is made available by the College of Optical Sciences and the University Libraries, The University of Arizona. If you have questions about titles in this collection, please contact [email protected]