Addressing #16

src/6_eigenvectors_QM.md

@@ -198,15 +198,16 @@ $$
 |\psi_2\rangle = \begin{pmatrix} \psi_{2,1} \\  \psi_{2,2} \\  \psi_{2,3} \\ \vdots \end{pmatrix} \,, \quad \ldots \, , |\psi_n\rangle = \begin{pmatrix} \psi_{n,1} \\  \psi_{n,2} \\  \psi_{n,3} \\ \vdots \end{pmatrix} \, .
 $$
 
-An important property of eigenvalue equations is that if you have two eigenvectors
-$ |\psi_i\rangle$ and $ |\psi_j\rangle$ that have associated *different* eigenvalues,
-$\lambda_{\psi_i} \ne \lambda_{\psi_j}  $, then these two eigenvectors are orthogonal to each
-other, that is
-$$
-\langle \psi_j | \psi_i\rangle =0 \, \quad {\rm for} \quad {i \ne j} \, .
-$$
-This property is extremely important, since it suggest that we could use the eigenvectors
-of an eigenvalue equation as a *set of basis elements* for this Hilbert space.
+!!! tip "Orthogonality of eigenvectors"
+    An important property of eigenvalue equations is that if you have two eigenvectors
+    $ |\psi_i\rangle$ and $ |\psi_j\rangle$ that have associated *different* eigenvalues,
+    $\lambda_{\psi_i} \ne \lambda_{\psi_j}  $, then these two eigenvectors are orthogonal to each
+    other, that is
+    $$
+    \langle \psi_j | \psi_i\rangle =0 \, \quad {\rm for} \quad {i \ne j} \, .
+    $$
+    This property is extremely important, since it suggest that we could use the eigenvectors
+    of an eigenvalue equation as a *set of basis elements* for this Hilbert space.
 
 Recall from the discussions of eigenvalue equations in linear algebra that
 the eigenvectors $|\psi_i\rangle$ are defined *up to an overall normalisation constant*. Clearly, if $|\psi_i\rangle$ is a solution of $\hat{A}|\psi_i\rangle = \lambda_{\psi_i}|\psi_i\rangle$