Gaussian system

Create File 10-1 using an editor independent of the GAUSSIAN system and use it to solve Exercise 10-1. 

Entering Gaussian System, Link 0=g94 Input=h2o.com 0utput=h2o.log Initial command ... 

The system of quantities usually associated with cgs units is called the Gaussian system that associated with SI is often called 4D. 

There is usually no problem in converting between 4D and Gaussian quantities until we have to consider electrical and magnetic phenomena. In the Gaussian system we take the proportionality constant in Coulomb s law to be unity (a number),... 

Ziabicki, A Walasek, J, Topological Structure and Physical Properties of Permanently Cross-Linked Systems. 1. s-Functional, Homogenerous, Gaussian Systems, Macromolecules 11, 471, 1978. 

In the present book, for magnetism we use the SI unit that is based on the MKS A (meter, kilogram, second, ampere) system. In accordance with that, the tesla (1T = 10" gauss) was presented as the magnetic unit in Chapter 17 (see Fig. 17.10a and b). It is useful to know both the SI and Gaussian systems and be able to convert between them. Thus, when one attempts to solve a magnetics problem, to avoid errors one is well advised to stick to a single convenient unit system. A useful conversion table of... 

We shall use mainly the cgs Gaussian system of units. This is a mixed system with electrical quantities measured in cgs electrostatic units (esu) and magnetic quantities measured in cgs electromagnetic units (emu). 

The two common unit systems employed for the description of nonlinear optical properties are the SI (or MKS) and Gaussian (or cgs) systems (Boyd24 mentions an alternative system of SI units that are not discussed further in this article, as it has not been used with organometallic complexes). In the Gaussian system, properties are described in units of esu. 

The main source of confusion arises from the fact that not only do the units vary between each system, but the dimensions of the properties also vary for example, the polarizability a has dimensions of length cubed in the Gaussian system (units cm3) but dimensions of charge times length squared times inverse potential (units C m2 V 1) in the SI system. Furthermore, vacuum permittivity e0 exists in the SI system (having units of F m ) but has no equivalent in the Gaussian system (i.e., e0 = 1). It is important to be able to convert between the two systems, but care must be taken to ensure not only that the units are converted correctly but also that the quantities of interest are treated according to their different definitions in different systems. 

The dimensions of the first-, second-, and third-order susceptibilities in both systems are simply derived from the polarizability power series equation.24 In the Gaussian system, polarization P and electric field strength E have equivalent dimensions [units statV cm 1 = statC cm 2 = (erg cm 3)112] and are related by... 

Similarly, the units for a, /3, and y in both SI and Gaussian systems can be derived from the equation describing polarization on the molecular scale (noting units nsl C m, and units ficgs statV cm2) and are given in Table I. To convert y(1), x z and, y(3) between the systems of units, it is also... 

Other systems of units and equations in common use in electromagnetic theory, in addition to the SI, are the esu system, the emu system, the Gaussian system, and the system of atomic units. The conversion from SI to these other systems may be understood in the following steps. 

The Gaussian system is a mixture of the esu system and the emu system, expressed in terms of three base units, esu being used for quantities in electrostatics and emu for electrodynamics. It is thus a hybrid system, and this gives rise to complications in both the equations and the units. 

In the usual form of the Gaussian system, the following quantities are defined as in the esu system charge Q, current /, electric field E, electric displacement Z)(ir), electric potential V, polarization P, electric dipole moment p, electric susceptibility /e(ir), polarizability [Pg.119]

The transformations of the more important equations between the Gaussian system and the SI are given in table 7.4 below. 

We prefer to use the gaussian system in applications to atomic phenomena. (In any event, it will not matter once we change to atomic units.) Since the Coulomb attraction is a central force (dependent only on / ), the potential energy is related by... 

In this equation the sums are over all particles of the molecule (electrons and nuclei), and mu Vu Qu At and Rt are mass, velocity, electric charge, vector potential of the exterior magnetic field, and position vector of particle number i, respectively, c is the velocity of light (the Gaussian system of units will be used throughout). 

The above considerations leads to the somewhat troubling question of whether (128) represents the true non-relativistic limit of the Dirac equation in the presence of external fields. Referring back to (110) we have certainly obtained the non-relativistic limit of the free-particle part Lm, but we have in fact retained the interaction term as well as the Lagrangian of the free field. In order to obtain the proper non-relativistic limit, we must consider what is the non-relativistic limit of classical electrodynamics. This task is not facilitated by the fact that, contrary to purely mechanical systems, the laws of electrodynamics appear in different unit systems in which the speed of light appears differently. In the Gaussian system Maxwell s laws are given as... 

Since, starting from the Gaussian system of units, there are 3 basic units, but 4 fundamental constants, there are more possibilities to define atomic units, in addition to that proposed by Hartree. Rather than basing this system on h, m, and e, one may choose h, m, and c as the basic units, such that in this natural or relativistic system gets the value a and is then called the coupling strength. 

To construct this limit we can proceed as we did for the nrl of the Dirac equation. We choose a system of units, for which in the Maxwell equations only appears, but not c. There are two allowed choices, either b — c or 6 = 1, but not b = c like in the Gaussian system. 

Gaussian system of units - A hybrid system used in electromagnetic theory, which combines features of both the esu and emu systems. 

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