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Year 1·Month 14·Week 1

Day 365: Free Particle - Time-Independent Schrödinger Equation

Day 365 of 2,016~12 min read

Learning Objectives

•**Derive the time-independent Schrödinger equation** for a free particle (V=0)
•**Solve the TISE** to obtain plane wave solutions
•**Interpret the dispersion relation** E = ℏ²k²/2m physically
•**Explain why the spectrum is continuous** rather than discrete
•**Distinguish traveling waves from standing waves** in the free particle context
•**Visualize plane waves** and understand their physical meaning

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