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Quantum Engineering Year 0: Mathematical Foundations Month 5Day 116

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Year 0·Month 5·Week 1

Day 116: The Spectral Theorem — Foundation of Quantum Measurement

Day 116 of 2,016~10 min read

Learning Objectives

•State and prove the spectral theorem for Hermitian operators
•Understand spectral decomposition: A = Σλᵢ Pᵢ
•Apply spectral theorem to compute matrix functions
•Connect spectral decomposition to quantum measurement postulates
•Work with projection operators and resolutions of identity
•Compute functions of Hermitian matrices (e.g., e^A, √A)

Today's Schedule (7 hours)

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1 Statement of the Spectral Theorem 2 Proof Outline 3 Projection Operators 4 Spectral Decomposition 5 Functions of Hermitian Operators 6 Computing Spectral Decomposition Quantum Mechanics Connection The Measurement Postulate Example Measuring _z on x Uncertainty Principle from Spectral Theory

Day 115Day 116 of 2,016Day 117