Tunable laser Stark-difference spectra of CD3OH

We present Doppler resolution limited spectra of the P(J) and R(J) multiplets for J ≦ 10 of the 10-μm CO stretch band of ¹²CD₃¹⁶OH using a tunable diode laser. Relative frequencies within the multiplets accurate to ±0.0002–0.0005 cm^?1 are obtained, but no absolute frequencies are given. We are able to assign most of the hindered rotation and K substructure in these multiplets. The assignments are based on analyses of Stark-difference spectra combined with the ground-state microwave data and the intensity variations which are expected theoretically. The ground and excited state A, K = 1 asymmetry splitting parameters are measured to be δ₁″ = (8.5450 ± 0.0080) × 10^?3cm^?1 and δ₁′ = (9.7706 ± 0.0080) × 10^?3cm^?1, respectively. The ground-state value agrees well with the microwave results. A rapid-scan system for recording data and a computer-aided technique for calibrating and plotting the spectra are described.     

Certain Jordan operator algebras and double commutant theorems

Two operations on sets of bounded operators on Hilbert space are studied: One produces Jordan algebras and the other, its inverse in a certain sense, produces self-adjoint linear spaces. The question of which Jordan algebras arise from the first of these operations is investigated. It is shown that, in many cases, R has this property if and only if the complex associative algebra R + iR is equal to its double commutant. Thus, a by-product of the study is another approach to double commutant theorems.     

The reduction of the multi-dimensional schrödinger equation to a one-dimensional integral equation

A method is proposed for reducing the multi-dimensional Schrödinger equation to a one-dimensional integral equation. The reduction is exact; and the resulting integral equation although complicated, may be treated by any of a number of numerical methods. Two 2-dimensional problems, the harmonic oscillator and the S-limit for helium and one 3-dimensional problem, the helium ground state are treated in this way.