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Quantum Engineering Year 1: Quantum Mechanics Core Month 13Day 347

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Year 1·Month 13·Week 2

Day 347: Compatible Observables and Simultaneous Measurements

Day 347 of 2,016~18 min read

Learning Objectives

•Define compatible observables in terms of the commutator condition [A, B] = 0
•Prove that commuting operators share a complete set of common eigenstates
•Construct and verify simultaneous eigenstates for compatible observables
•Explain the concept of Complete Set of Commuting Observables (CSCO)
•Identify physical examples of compatible and incompatible observables
•Connect compatibility to the possibility of simultaneous precise measurements

Today's Schedule (7 hours)

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On this page

1 The Fundamental Question of Simultaneous Measurement 2 The Commutator 3 Definition of Compatible Observables 4 The Fundamental Theorem 5 Physical Interpretation 6 The Degenerate Case 7 Complete Set of Commuting Observables CSCO 8 Physical Examples of Compatible Observables Example 1 Energy and Angular Momentum Central Potential Example 2 Momentum Components Example 3 Position Components 9 Examples of Incompatible Observables Example 1 Position and Momentum Same Component Example 2 Angular Momentum Components Example 3 Position and Energy Bound States Quantum Computing Connection Compatible Observables in Quantum Information Stabilizer Formalism Multi-Qubit Compatible Measurements

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