A positive muon (charge

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · The formalism of quantum mechanics

The Structure of Quantum Mechanics, Ch Charged particles in electromagnetic fields

Problem

A positive muon (charge q=+eq=+e, mass mμ=1.884×10−28 kgm_\mu = 1.884\times10^{-28}\,\mathrm{kg}) moves in a uniform field B⃗=Bz^\vec B = B\hat z, B=0.80 TB=0.80\,\mathrm T, described in the Landau gauge A⃗=(0,Bx,0)\vec A = (0, Bx, 0). ((a)) Write the minimally coupled Hamiltonian H^=12mμ(p⃗^−qA⃗)2\hat H = \frac{1}{2m_\mu}(\hat{\vec p}-q\vec A)^2 explicitly in this gauge. ((b)) Evaluate ∣[π^x,π^y]∣/ℏ|[\hat\pi_x,\hat\pi_y]|/\hbar, in SI units. ((c)) Evaluate the Landau-level degeneracy per unit area, n=eB/hn=eB/h, in m−2\mathrm{m}^{-2}.

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