Where Eigenvalues Pay Rent
Part 1 built the spectral theorem. Before we survey the tools that compute eigenvalues, here is why you would want to: three industries, three matrices, three ways the same decomposition does real work.
Index¶
How to Raise e to a Matrix (and Why You'd Want To)
A first-principles account of why \(\lvert\psi(t)\rangle = e^{-iHt}\lvert\psi_0\rangle\) solves the Schrödinger equation, and what that formula means geometrically. The whole story is carried by one running example, the \(2\times2\) Hermitian matrix \(H=\begin{pmatrix}2&1\\1&2\end{pmatrix}\).