Ground-state probability ($P_1=|⟨{\varphi }_1,\psi ⟩{|}^2$)

The probability that an energy measurement selects a ground state. For a nondegenerate normalized mode ${\varphi }_1$, it is $|⟨{\varphi }_1,\psi ⟩{|}^2$; for a degenerate ground eigenspace, use its full orthogonal projection.