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Quantum Engineering Year 1: Quantum Mechanics Core Month 13Day 362

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Year 1·Month 13·Week 4

Day 362: The Heisenberg Picture — Operators Evolve, States Fixed

Day 362 of 2,016~15 min read

Learning Objectives

•Define the Heisenberg picture and relate it to the Schrodinger picture
•Derive the Heisenberg equation of motion for operators
•Solve operator equations of motion for simple systems
•Connect the Heisenberg equation to classical Hamilton equations
•Prove equivalence of expectation values between pictures
•Apply the Heisenberg picture to harmonic oscillator dynamics

Today's Schedule (7 hours)

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On this page

1 The Heisenberg Picture Definition 2 Transformation Between Pictures 3 The Heisenberg Equation of Motion 4 Connection to Classical Mechanics 5 Equations of Motion for Position and Momentum 6 Conservation of Commutation Relations 7 The Harmonic Oscillator in Heisenberg Picture 8 Creation and Annihilation Operators in Heisenberg Picture Physical Interpretation Operators as Dynamical Variables Classical Limit Made Transparent Matrix Mechanics Origin Quantum Computing Connection Gate Synthesis via Heisenberg Evolution Clifford Gates and Stabilizer Formalism Error Propagation

Day 361Day 362 of 2,016Day 363