Commit f0ef9f67 authored by Isidora Araya's avatar Isidora Araya
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Update 13_semiconductors_solutions.md

parent a248c5a8
......@@ -20,8 +20,8 @@ Holes near the top of the valence band have a positive effective mass, their ene
The equation of motion for an electron near the bottom of the conduction band is:
$$m_{eff} \frac{d\mathbf{v}}{dt} = -e\mathbf{v} \times \mathbf{B}$$
and when replacing we get two coupled equations:
$$\dot{k_x} = \frac{e \hbar}{m_eff}B k_y$$
$$\dot{k_y} = -\frac{e \hbar}{m_eff}B k_x$$
$$\dot{k_x} = \frac{e}{m_eff}B k_y$$
$$\dot{k_y} = -\frac{e}{m_eff}B k_x$$
The solution to this equation is circular motion of cyclotron frequency of $\omega_c = \frac{eB}{m_{eff}}$, where the Lorentz
force is perpendicular to $\nabla_\mathbf{k} E$.
......
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