Introduction to Quantum Mechanics · Problem A.5
Afterword — David J. Griffiths
Physics — Quantum Mechanics · inner-products
Problem
Prove the Schwarz inequality (Equation A.27):
∣⟨α∣β⟩∣2≤⟨α∣α⟩⟨β∣β⟩.
Hint: Let ∣γ⟩=∣β⟩−(⟨α∣β⟩/⟨α∣α⟩)∣α⟩, and use ⟨γ∣γ⟩≥0.
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