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Quantum Engineering Year 1: Quantum Mechanics Core Month 14Day 379

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Year 1·Month 14·Week 3

Day 379: Quantum Harmonic Oscillator — Setup & Motivation

Day 379 of 2,016~17 min read

Learning Objectives

•Review the classical harmonic oscillator and its phase space behavior
•Write the quantum Hamiltonian for the harmonic oscillator
•Introduce dimensionless variables to simplify the problem
•Understand why the QHO is fundamental to physics (Taylor expansion)
•Recognize the QHO in molecular, optical, and solid-state systems
•Compare classical and quantum oscillator behavior computationally

Today's Schedule (7 hours)

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On this page

1 The Classical Harmonic Oscillator Classical Equation of Motion Classical Hamiltonian Key Classical Properties 2 Why the Harmonic Oscillator Is Ubiquitous Taylor Expansion of Any Potential Physical Examples 3 The Quantum Hamiltonian The Time-Independent Schrodinger Equation 4 Introducing Dimensionless Variables Characteristic Length Characteristic Energy Dimensionless Position Dimensionless Schrodinger Equation 5 Asymptotic Behavior 6 Preview of Results Energy Eigenvalues Physical Origin of Zero-Point Energy 7 Quantum Computing Connection Bosonic Qubits Fock Encoding Physical Platforms

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