By Laverne A.
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Example text
34) obtenue grˆ ace ` a l’analogie formelle avec le potentiel ´electrostatique ordinaire d’une distribution de charge. En r´esum´e, il est toujours possible de d´ecrire un champ ´electromagn´etique par des potentiels dans la jauge de radiation, c’est-`a-dire qui, dans le vide (hors des sources du champ), ont les propri´et´es φ(r, t) ∇ · A(r, t) = 0 = 0. 35) seule d´efinit la jauge de Coulomb. Mais notre choix, plus sp´ecifique, satisfait aussi 1 ∇ · A + 2 ∂t φ = 0, c c’est-`a-dire la condition de jauge de Lorenz.
Ii ) V´erifiez que les champs E et B sont encore les mˆemes. iii ) Mˆemes questions pour passer `a φ′′ = −V x, A′′ = (V t, Bx, 0), o` u V est une constante. 7. A propos des moments angulaire orbital et de spin d’un quanton. df i ) V´erifiez que la propri´et´e [Ri , Pj ] = i¯hδij et la d´efinition L = R ∧ P impliquent hεijk Lk . [Li , Lj ] = i¯ df ii ) V´erifiez que la propri´et´e [Ji , Jj ] = i¯hεijk Jk et la d´efinition S = J − L impliquent [Si , Sj ] = i¯ hεijk Sk . iii ) Montrez que [Ji , Rj ] = i¯ hεijk Rk et [Ji , Pj ] = i¯hεijk Pk .
42) o` u nx , ny et nz sont des entiers alg´ebriques. C’est le choix le plus commode lorsqu’on a `a faire ` a un rayonnement qui se propage. L’autre cas pratique important est celui d’une cavit´e r´esonante, bien r´eelle, ou d’un guide d’onde. Ce sont alors les modes stationnaires qui nous int´eressent plutˆot, obtenus par des conditions aux limites qui d´ependent de la nature physique du champ consid´er´e ( A, E ou B en ´electrodynamique) et des parois (constitu´ees de conducteur plus ou moins parfait).
Rayonnement quantique by Laverne A.
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