## Classical Piano Music For Stanford

Let's consider a field E waves, the falling wave consisting from with a frequency and from two scattered waves from and. We will designate amplitudes of these waves respectively through, and, using identical indexes for wave vectors and phases. The casual field can be described by expression

The first anti-Stokes AS1 line corresponding to the first Stokes S1 line finds a strong maximum of intensity at an angle of dispersion about 3,0 °. Apparently, anti-Stokes dispersion does not happen in correction of an incident light, and after a maximum quickly falls down to zero.

The wave mechanism of the Raman dispersion in interaction of a molecule capable to resonant fluctuation with a frequency (or to several such fluctuations), with the falling and waves. Molecular vibration can be presented in the form as fluctuation of a point with x (the point is one of atoms of a having the mass of t), with the coefficient of attenuation of R and elastic effort returning a point in balance. Under the influence of the external periodic force resulting from a with a casual field of a wave E the movement which is described by the equation is created

Dispersion in the anti-Stokes party is observed in the form of the concentric rings surrounding a laser beam of light. The subsequent rings correspond a with a bigger frequency (shorter wavelength). Stokes dispersion has various directions, but the greatest intensity of light on the direction of the falling bunch.

laziness. Otherwise business with anti-Stokes dispersion which is described by expression is (When performing a condition continuous arrival of energy to an wave will be guaranteed only if

According to this expression anti-Stokes light along a cone which axis coincides with an incident light, and — a corner between this and the direction forming a cone. On the screen,

The first Stokes S1 line finds the greatest intensity in the direction of a laser beam. In process of increase of a corner intensity decreases and does not find other maximum in any certain direction. (Emergence of maxima in the subsequent Stokes S2 and S3 lines, and also very weak maxima on the S1 line has the special reason which we will not discuss here.)

where and — wave vectors of the falling and disseminated waves — spatial coordinate, and — coordinate. Strong interaction of this wave can happen to a molecule only near a resonance, and consequently, with a frequency in an infrared which is the frequency of beats. Therefore for calculation of force of F we will use only that part of the general expression which contains differential frequency. The general expression has an appearance

, and have precisely certain directions. While anti-Stokes photons have really precisely certain, Stokes photons dissipate in various directions, the main thing 0'brazom in the direction of the falling beam. Tsayger with employees was offered by the mechanism of process of the Raman dispersion. Thus each step is a two-photon in which two photons and a photon take part. To the last there corresponds the wave vector of the wave arising from the coherent molecular vibrations excited by the falling optical wave. The first step consists in formation of a Stokes photon and phonon from the first laser photon: