# Relativistic Quantum Mechanics: Wave Equations by Professor Dr. Walter Greiner (auth.)

By Professor Dr. Walter Greiner (auth.)

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121), and they result in o = ~* [ - gllV (O=v + ~: Av) (0~1l + ~: All ) ] ~ IlV ( a ie ) (a ie )] ~ * - ~ [- g OXV - lie Av . I. 1. 1. e V'f' One calls . 1. 123) the four-current density in the electromagnetic field Av. Obviously, the following relation holds: gl-'V ~jv = ~pL = 0 ax I-' ax I-' . 124) This is a continuity equation for the four-current density, usually its meaning is that of a conservation law. 123)] yields charge conservation. 34), if we exclude the tenn proportional to Av. 36).

3, 71"0 -/+ 3, (17) . (14) We can understand both the allowed as well as the forbidden processes by assuming the conservation of C A A_I C£elm C = £elm . (18) The positive C parities of 71"0 and 'rJ follow from the existence of the decays (13) using (12). 82) that positively charged particles possess a large upper component in the nonrelativistic limit (I

100)]. tjj(+) = tjj(-) = Jv (~) [*(p . r+Ept)] exp r - Again each linear combination charge + 1 ,charge-l is a normalized eigenfunction of the momentum p with charge +I, and each linear combination with In 112 -I n21 2 = -1 is a normalized solution with charge -1. 9) by ni = 0, ± 1, ± 2, ... g. L: p means L:Pi ' The index A = +1 denotes a positive charge state whereas A = -1 denotes a negative one. 114) form a complete orthonormalized system. 114). Let us now consider a general state tjj containing particles with positive as well as negative charge.