From 9330916027427583ffd31964278850a113cb4773 Mon Sep 17 00:00:00 2001 From: Umut Kalkan <umut.kalkan@live.nl> Date: Tue, 6 Apr 2021 18:23:27 +0000 Subject: [PATCH] Update 11_nearly_free_electron_model.md bold, italic text fix --- src/11_nearly_free_electron_model.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/11_nearly_free_electron_model.md b/src/11_nearly_free_electron_model.md index 95726ff2..f51a321d 100644 --- a/src/11_nearly_free_electron_model.md +++ b/src/11_nearly_free_electron_model.md @@ -93,7 +93,7 @@ In this figure, the orange curves represent the nearly-free electron dispersion, ### Analyzing the avoided crossings -*Remark: An avoided crossing is an important concept in quantum mechanics that can be analyzed using **perturbation theory**. You will only learn this theory later in QMIII, so we will need to postulate some important facts here.* +*Remark: An avoided crossing is an important concept in quantum mechanics that can be analyzed using ***perturbation theory***. You will only learn this theory later in QMIII, so we will need to postulate some important facts here.* To analyze what happens near the crossings, we first neglect the lattice potential and consider the free-electron dispersion near the crossing at $k=\pi/a$ in 1D. Near this crossing, we see that two copies of the dispersion come together (one copy centered at $k=0$, the other at $k=2\pi/a$). We call the corresponding plane-wave eigenfunctions $|k\rangle$ and $|k'\rangle =|k-2\pi/a\rangle$. We now express the wavefunction near this crossing as a linear superposition $|\psi\rangle = \alpha |k\rangle + \beta |k'\rangle$. Note that this wave function is very similar to that used in the LCAO model, except there we used linear combinations of the orbitals $|1\rangle$ and $|2\rangle$ instead of the plane waves $|k\rangle$ and $|k'\rangle$. -- GitLab