Day 370: Position and Momentum Space

Learning Objectives

• •**Transform between position and momentum representations** using Fourier transforms
• •**Express operators in both representations** (x̂ in p-space, p̂ in x-space)
• •**Apply completeness relations** to expand states
• •**Calculate expectation values** in either representation
• •**Use the FFT** for practical momentum-space calculations
• •**Understand the deep duality** between position and momentum

Today's Schedule (7 hours)