Physics · Quantum Mechanics
Consider an arbitrary unnormalized wavefunction ψ, expanded in terms of the orthonormal eigenstates |φ n ⟩ of a Hamiltonian H, where H|φ n ⟩ = ε n |φ n ⟩ for n = 0, 1, 2, ... and ε 0 ≤ ε 1 ≤ ε 2 ... If ψ = ∑ n a n |φ n ⟩, which of the following inequalities definitely holds for any set of coefficients a n ?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1∑ n a n ε n ∑ n |a n | 2 < ε 0
- 2∑ n a n ε n ∑ n |a n | ≥ ε 0
- 3∑ n |a n | 2 ε n ∑ n |a n | 2 ≥ ε 0✓
- 4∑ n |a n | 2 ε n ∑ n |a n | 2 < ε 0
Correct answer
∑ n |a n | 2 ε n ∑ n |a n | 2 ≥ ε 0
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