From f0ef9f67665f2ded009d17beaac70fc4678afaa4 Mon Sep 17 00:00:00 2001 From: Isidora Melania Araya Day <isidora.araya@ug.uchile.cl> Date: Tue, 31 Mar 2020 09:53:55 +0000 Subject: [PATCH] Update 13_semiconductors_solutions.md --- src/13_semiconductors_solutions.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/13_semiconductors_solutions.md b/src/13_semiconductors_solutions.md index 3b95a6bf..357b9397 100644 --- a/src/13_semiconductors_solutions.md +++ b/src/13_semiconductors_solutions.md @@ -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 $\nabla_\mathbf{k} E$. -- GitLab