PARTICELLA CARICA IN UN CAMPO ELETTROMAGNETICO ...
PARTICELLA CARICA IN UN CAMPO ELETTROMAGNETICO ...
PARTICELLA CARICA IN UN CAMPO ELETTROMAGNETICO ...
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9/1 <strong>PARTICELLA</strong> <strong>IN</strong> <strong>UN</strong> <strong>CAMPO</strong> <strong>ELETTROMAGNETICO</strong> 11/12 2Campo magnetico costante e uniformeSe E(x, t) = 0, B(x, t) = B 0si può prendereV = 0,A = 1 2 B 0 ∧ x (∇·A = 0).Poiché B 0 ∧ ˆx · ˆp = B 0 · ˆx ∧ ˆp = B 0· ˆl = ħ B 0· ˆl l’espressione (2) diventa(3) Ĥ = ˆp22m − ħq2mc B 0· ˆl +q28mc 2 (B 0 ∧ ˆx) 2 + Û.Per l’elettrone q = −e 0 , m = m e ,e quindie 0 ħ2m e c = µ B(4) Ĥ = ˆp22m e+ µ B B 0· ˆl + e2 08m e c 2 (B 0 ∧ ˆx) 2 + Û.Per campi B 0 sufficientemente deboli(5) Ĥ = ˆp22m e+ µ B B 0· ˆl + Û.