Section 5.11 Evolution Equation
The simplest non-trivial ode is the first-order linear ode with constant coefficients:
We can generalize this equation to apply to solutions which are exponentials (Section 5.10), i.e.:
is a solution of:
where \(A\) is a suitable constant matrix. (Show that if \(A\) is anti-Hermitian, then \(M(x)\) is unitary.)
Example Problem: Find the matrix differential equation that has the solution:
where \(H\) is Hermitian. Do you recognize your differential equation?