Fix Landau Zener fromula

src/adiabatic_landau_zener.md

@@ -38,8 +38,8 @@ From the adibatic theorem, we know that the system will remain in the $n-th$ eig
 Consider a two level system described by the Hamiltonian,
 $$
 H(t) = \left( \begin{array}{cc}
-vt & \Delta \\
-\Delta & -vt
+vt/2 & \Delta \\
+\Delta & -vt/2
 \end{array}
 \right).
 $$
@@ -50,7 +50,7 @@ $$
 
 Landau and Zaner found an explicit expression that describes the probability of tuneling to a high energy state as $t\rightarrow \infty$. It is
 $$
-P \sim e^{-\frac{\pi}{2v h} \frac{\Delta}{E_0-E_1}}.
+P \sim e^{-2\pi \frac{|Delta|^2}{\hbar |v|}}.
 $$
 Here, $\Delta = \langle 0 | H |1 \rangle$, and $v=d(E_0(t)-E_1(t))/dt$. From the adiabatic theorem, we recall that when the system evolves in an adiabatic way, it will remain in the initial eigenstate as shown in the animation below.