| Chapter | Classic Problem | Why the Solution is Non-Trivial | |---------|----------------|--------------------------------| | 3 | 3.15 – Harmonic oscillator via ladder operators | Requires algebraic recursion and normalization constants. | | 5 | 5.9 – Angular momentum addition | Clebsch-Gordan coefficients and CG table usage. | | 7 | 7.4 – Stark effect for hydrogen | Perturbation theory with degenerate states and matrix diagonalization. | | 9 | 9.2 – WKB connection formulas | Careful handling of Airy functions and turning points. | | 12 | 12.6 – Born approximation for Yukawa potential | Fourier transform of exponential potential. | | 14 | 14.3 – Dirac equation free particle | Gamma matrices, spinors, and positive/negative energy solutions. |
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