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Quantum Engineering Year 1: Quantum Mechanics Core Month 16Day 423

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Year 1·Month 16·Week 1

Day 423: Free Particle in 3D

Day 423 of 2,016~8 min read

Learning Objectives

•Solve the radial equation for V(r) = 0
•Identify spherical Bessel functions of the first and second kind
•Understand the partial wave expansion of a plane wave
•Apply asymptotic forms for large arguments
•Connect to scattering theory foundations
•Recognize these functions in physics applications

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The Free-Particle Radial Equation Change of Variable kr Solutions Spherical Bessel Functions Explicit Forms Asymptotic Behavior Spherical Hankel Functions Plane Wave Expansion Free Particle Wavefunctions Quantum Computing Connection Quantum Simulation of Scattering Encoding Angular Momentum

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