Experimental and Theoretical Studies in Planetary Aeronomy Quarterly Progress Report, 24 May - 31 Aug. 1968

Determining absorption and photoionization cross sections of planetary gases - planetary aeronomy researc

Definition Research Study

Data were complied on the physical behavior and characteristics of plasma gas and/or dust in the context of how they relate to the self-contamination of manned orbiting vehicles. A definition is given of a systematic experimental program designed to yield the required empirical data on the plasma, neutral gas, and/or the particulate matter surrounding the orbiting vehicles associated with shuttle missions. Theoretical analyses were completed on the behavior of materials to be released from the orbiting or subsatellite shuttle vehicles. The results were used to define some general experimental design recommendations directly applicable to the space shuttle program requirement. An on-board laser probe technique is suggested for measuring the dynamic behavior, inventory, and physical characteristics of particulates in the vicinity of an orbiting spacecraft. Laser probing of cometary photodissociation is also assessed

Quantum Systems and Alternative Unitary Descriptions

Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We show how different invariant Hermitian scalar products give rise to different descriptions of a quantum system in the Ehrenfest and Heisenberg picture.Comment: 18 page

Experimental and theoretical studies in planetary aeronomy Quarterly progress report, 1 Sep. - 30 Nov. 1968

Laboratory and theoretical studies in planetary aeronom

Experimental and theoretical studies in planetary aeronomy Final report, 17 Sep. 1966 - 1 Mar. 1968

Photochemistry of planetary atmospheric matter, solar EUV and VUV spectral region studies, ion-molecule reactions and photoionization products, and planetary aeronomy investigation

Quantum Bi-Hamiltonian Systems

We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the associative version of Nijenhuis tensors. Explicit examples, e.g. for the harmonic oscillator, are given.Comment: 14 pages; the paper is posted for archival purpose

Contractions: Nijenhuis and Saletan tensors for general algebraic structures

Generalizations in many directions of the contraction procedure for Lie algebras introduced by E.J.Saletan are proposed. Products of arbitrary nature, not necessarily Lie brackets, are considered on sections of finite-dimensional vector bundles. Saletan contractions of such infinite-dimensional algebras are obtained via a generalization of the Nijenhuis tensor approach. In particular, this procedure is applied to Lie algebras, Lie algebroids, and Poisson structures. There are also results on contractions of n-ary products and coproducts.Comment: 25 pages, LateX, corrected typo

Experimental and theoretical studies in planetary aeronomy Final report

Planetary aeronomy - photochemistry of planetary atmosphere, vacuum and extreme ultraviolet spectral regions, and theoretical aeronom

The nonlinear superposition principle and the Wei-Norman method

Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei-Norman method is applied to obtain the associated differential equation in the group $SL(2,R)$. The superposition principle for first order differential equation systems and Lie-Scheffers theorem are also analysed from this group theoretical perspective. Finally, the theory is applied in the solution of second order differential equations like time-independent Schroedinger equatio