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Derivation of the quantization of the EM field in a dielectrics
I'm currently studying the quantization of the EM field in a dielectric medium and trying to understand the quantization scheme of Huttner and Barnett (1992, see Phys. Rev. A 46, 4306). The system ...
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How to prove that momentum eigenstates are also eigenstates of asymmetric Landau Hamiltonian?
$$H(B,E)=\frac{1}{2m}p_x^2+\frac{1}{2m}\left(p_y-\frac{q}{c}Bx\right)^2-qEx$$
This Hamiltonian commutes with $p_y$, therefore, $\langle y|k_y\rangle=e^{ik_yy}$ are eigenstates of $H$, but how can I ...
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Lorentz force derivation in quantum mechanics [closed]
In Sakurai and Napolitano, chapter 2, there's a derivation of the QM Lorentz force.
Given $$H=\frac{1}{2m}\left(\mathbf{p}-\frac{e\mathbf{A}}{c}\right)^2+e\phi = \frac{\mathbf{\Pi}^2}{2m}+e\phi$$
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