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Quantum EngineeringYear 1: Quantum Mechanics CoreMonth 14Day 366

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Year 1·Month 14·Week 1

Day 366: Plane Waves & Normalization

Day 366 of 2,016~12 min read

Learning Objectives

  • •**Explain why plane waves cannot be normalized** in the conventional sense
  • •**Apply box normalization** and understand the limit L → ∞
  • •**Use delta-function normalization** for momentum eigenstates
  • •**Prove orthogonality relations** for both normalization conventions
  • •**Connect momentum and position eigenstates** through Fourier transforms
  • •**Compute normalization integrals** numerically and verify theoretical predictions

Today's Schedule (7 hours)

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On this page

1 The Normalization Problem2 Physical Interpretation3 Box NormalizationStep 1 Impose Periodic Boundary ConditionsStep 2 Normalize in the BoxStep 3 OrthonormalityStep 4 The Limit L4 Delta-Function Normalization5 Wave Number vs Momentum Conventions6 Completeness Relations7 Position Eigenstates8 Expansion in Momentum EigenstatesQuantum Computing ConnectionQuantum Fourier TransformContinuous-Variable Systems
Day 365Day 366 of 2,016Day 367