Quantum variational principle
= Quantum variational principle
For every normalized trial state $\psi$ in the domain of a <Hamiltonian operator> $H$ that is bounded below,
$$
E_0\leq\langle\psi,H\psi\rangle,
$$
where $E_0$ is the <ground-state energy>. Equality holds precisely when the trial state lies in the ground-state eigenspace.