A Simple Derivation of Schroedinger Uncertainty Relation

We show how the Schroedinger Uncertainty Relation for a pair of observables can be deduced using the Cauchy-Schwarz inequality plus successive applications of the commutation relation involving the two observables. Our derivation differs from the original one in the sense that we do not need the expansion of the product of these two observables in a sum of symmetrical and anti-symmetrical operators.Comment: 1.5 pages, no figures, revtex4; v2: title slightly changed, published versio

Light Propagation in Nonlinear Waveguide and Classical Two-Dimensional Oscillator

The quantum optical problem of the propagation of electromagnetic waves in a nonlinear waveguide is related to the solutions of the classical nonstationary harmonic oscillator using the method of linear integrals of motion [ Malkin et.al., Phys Rev. 2D (1970) p.1371 ]. An explicit solution of the classical oscillator with a varying frequency, corresponding to the light propagation in an anisotropic waveguide is obtained using the expressions for the quantum field fluctuations. Substitutions have been found which allow to establish connections of the linear and quadratic invariants of Malkin et.al. to several types of invariants of quadratic systems, considered in later papers. These substitutions give the opportunity to relate the corresponding quantum problem to that of the classical two-dimensional nonstationary oscillator, which is physically more informative.Comment: 14 pages, including one Table, 29 bibliographic references; E-mail: [email protected]

Optical differentiation between cashmere and other textile fibres by laser diffraction

This paper reports a novel method to differentiate cashmere from synthetic fibres and even from other wool fibres with the help of laser diffraction patterns. In the diffraction pattern, only natural fibres depict additional spots above and below the actual diffraction plane. These spots can be used to distinguish different fibre materials by comparing their length-to-height aspect ratio with standard values. Especially, it can be recognized that the diffraction lines above and below the diffraction plane are significantly longer and finer for cashmere fibres than for any other wool