\( ~ 2 − 2m d 2 dr2 + V (r) + ~ 2 ℓ(ℓ + 1) uνℓ(r) = Eνℓuνℓ(r) (bound states) 2mr2 u (r) ∼ r ℓ+1 νℓ , as r → 0 .\)\( 1 Hˆ = 1 pˆ 2 + 2m 2 mω2xˆ 2 = ~ω Nˆ + 1 , 2 Nˆ = aˆ † aˆ aˆ = r mω 2~ xˆ + ipˆ mω , aˆ † = r mω 2~ xˆ − ipˆ , mω xˆ = r ~ 2mω (ˆa + aˆ † ) , pˆ = i r mω~ (aˆ † − aˆ),\)
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