Gaussian system of units

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). 

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). 

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. 

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

First consider the cgs Gaussian system of units. The hydrogen-atom Hamiltonian in these units is (assuming infinite nuclear mass)... 

We briefly summarize the units and dimensions in the Gaussian system of units for the most important quantities discussed in this book. This summary is fully redundant, since all of this information is already given in the book. However, it is spread over various places and we believe that it is convenient to have such a brief compilation available as a quick reference. In order to manipulate efficiently the units of almost all quantities relevant to the topic of this book, the most central relationship for the energy in mechanical and electromagnetic units... 

However, it may be noted in passing that Chestnut ° has given a powerful argument for the retention of the unrationalized cgs-Gaussian system of units— where, specifically, electromagnetic quantities are involved. 

The Hamiltonian for a one-electron system in a magnetic field described by the vector potential A is (in the Gaussian system of units)... 

It has been common for those who work in electromagnetic theory to use the Gaussian system of units consisting of selected cgs electromagnetic units (emu) and cgs electrostatic units (esu) to allow a comparison with results stated in the literature, we record here for convenience that the general division of use is [54]... 

The abbreviation au stands for atomic units , which is a system of units meant to simplify the equations of molecular and atomic quantum mechanics. The units of the au system are combinations of the fundamental units of mass (mass of the electron), charge (charge of the electron), and Planck s constant. By setting these three quantities equal to unity one gets simpler equations. The au system has a simple relation to the SI and Gaussian (cgs) systems of units. For example, 1 au of length = aQ (Bohr radius) = 5.29 x 10"9 cm =... 

A short digression on units is perhaps appropriate here. We shall use either Gaussian rrrrits in this book or, much more frequently, Hartree s atomic units. Gaussian units, as far as we are concerned, are identical with the old cgs system of units with the added proviso that charges are measured in unnamed electrostatic units, esu. The value of e is thus 4.803206808 X 10 esu. Keeping this number at hand is all that will be required to use Gaussian rmits in this book. 

So far we have employed gaussian units, which are more common in theoretical discussions. However, experimental results are generally discussed in terms of practical units. Since conversions between different systems of units can sometimes be confusing we include here an example. Consider R. In gaussian units E and are in statvolt/cm (for this is called gauss ), j in... 

In 1960, the eleventh General Conference on Weights and Measures recommended the International System of Units (Systeme International d Unites), abbreviated as SI units, for use in science SI units are essentially the rationalized mks system of units. Relations between SI units and Gaussian units are given in Table A.4 of the Appendix. Table A.5 allows one to convert equations from SI to Gaussian units. 

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 system of units most frequently employed in nonlinear optics is the Gaussian (or cgs) system. Sporadically, the SI unit system is used. It is important to be able to convert between the two systems. However, not only do the units need to be con-... 

One should avoid using non-SI units from the following unit systems the esu (electrostatic unit system), the emu (electromagnetic unit system) and the Gaussian unit system. However, equations relating these still widely used unit systems to the SI are listed in Chapter 7 of [1] which also makes extensive use of quantity calculus to help converting between those systems of units. 

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 units A system of units for electric and magnetic quantities based upon c.g.s. electrostatic and electromagnetic units. Although replaced by S1 units in most branches of science, they are, like Heavi-side-Lorentz units, still used in relativity theory and in particle physics. In Gaussian units, the electric and magnetic constants are both equal to unity. 

Table 1.2-11 deals with the relationship between CGS units and SI units, and lists those CGS units that were assigned special names. In the field of mechanics, the CGS system of units was built upon three quantities and their corresponding base units the centimeter, the gram, and the second. In the field of electricity and magnetism, units were expressed in terms of these three base units. Because this can be done in different ways, this led to the establishment of several different systems, for example the CGS electrostatic system, the CGS electromagnetic system, and the CGS Gaussian system. In those three systems, the system of quantities used... 

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