(Solution) - Prove that for a system with a nondegenerate ground state if -(2025 Original AI-Free Solution)

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Prove that, for a system with a nondegenerate ground state,

if ( is any normalized, well-behaved function that is not equal to the true ground-state wave function. Let b be a positive constant such that E1 + b < E2. Turn (8.4) into an inequality by replacing all Ek's except E1 with E1 + b. (The notation E1, E2( ( ( ( ( is as in Section 8.2.)