Applications of Finite Groups by J. S. Lomont (Auth.) PDF

By J. S. Lomont (Auth.)

ISBN-10: 1483231321

ISBN-13: 9781483231327

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Example text

As an example of the application of these transformations let us derive an equation from (2:1) and (2:2) and then transform it to obtain new equations. From (2:2a) one obtains by dividing by dV \w)T or T p \w)T p itm Τ^ T\bVJT = p_5\ \iV)T' (2:4a) (2:4b) 40 II. GROUPS Now considering F as a function of T and V we have from (2:2c) %=-S %=-P. , in (2:4) we get from this equation the following seven equations. >P)T ~~ \bTjP S+S\T>V)a B. [iSjy v v\7>s)v~\bv)a P^ P\7>TJP \7>PJT The Dirac Equation Let us consider the motion of a point particle of rest mass m0 according to the laws of classical special relativity theory.

2:10) If we let φ be a function of x, y, z, and t such that the y's (or a's) can operate on it, then the equation Ηφ = ίη Μ> (2:11) in which p is replaced in H by —ihV, is called the Dirac equation. Actually, a little more is required of the y's for this to be the Dirac equation, but these additional restrictions will be discussed later. As is well known, the Dirac equation (2:11) is the special relativistic wave equation describing the motion of a free electron, and φ is the electronic wave function.

Carmichael, R. D. (1937). " Ginn, New York. Cayley, A. (1897). " Cambridge Univ. Press, London and New York. Hilton, H. (1908). " Clarendon Press, Oxford. Kurosh, A. G. (1944). "Group Theory," (Eng. , 1955). Chelsea, New York. Ledermann, W. (1949). " Interscience, New York. Magnus, W. (1939). " B. G. Teubner, Leipzig. Magnus, W. " In preparation. Mathewson, L. C. (1930). " Houghton Mifflin, Boston. Mclntosh, H. V. (1955). Seminar in Group Theory (Notes). Aberdeen Proving Ground, Aberdeen, Maryland.

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Applications of Finite Groups by J. S. Lomont (Auth.)

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