Unformatted text preview: 2 , (ii) y 2 and (iii) xy with respect to the eigenstates of the system. 3. Consider a spinless particle of charge q and mass m moving in a uniform magnetic ﬁeld ~ B = B ˆ z . The Hamiltonian operator of the system is given by H = ± ~ p-q c ~ A ² 2 2 m where ~ B = ~ ∇× ~ A . It should be noted that diﬀerent deﬁnitions of the vector potential can yield the same uniform magnetic ﬁeld, e.g. (i) ~ A =-yB ˆ x , (ii) ~ A = xB ˆ y , and (iii) ~ A = B (-y ˆ x + x ˆ y ) / 2. Find the eigenenergies and eigenstates of the system for both case (i) and case (ii). It is clear that although the two sets of eigenenergies are identical, yet the two sets of eigenstates are very diﬀerent. Explain why such a system can have diﬀerent sets of energy eigenstates. —— End ——...
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- Spring '11
- Mass, feynman-hellmann theorem