4.4 Sphärische Besselfunktionen

Stellen die partikulären Lösungen der Besselschen Differentialgleichung dar. ^4.3

$$\sqrt{{\pi \over {2x}}} {1 \over 2} \left(\vphantom{-{1 \over x} {d \over {dx}}}\right. {1 \over x} {d \over {dx}} \left.\vphantom{-{1 \over x} {d \over {dx}}}\right)^{l}_{} {{\sin(x)} \over x}$$ (4.21)

$${{\sin(x)} \over x} {{\sin(x)}\over {x^2}} {{\cos(x)}\over x}$$ (4.22)

$$\left\{\vphantom{x^2{d^2 \over {dx^2}} + 2x {d \over dx} + \left[x^2-l(l+1)\right]}\right. {d^2 \over {dx^2}} {d \over dx} \left[\vphantom{x^2-l(l+1)}\right. \left.\vphantom{x^2-l(l+1)}\right] \left.\vphantom{x^2{d^2 \over {dx^2}} + 2x {d \over dx} + \left[x^2-l(l+1)\right]}\right\}$$ (4.23)

$${{l+1} \over x}$$ (4.24)

$$\int_{0}^{\infty} {\pi \over {2x^2}} \delta$$ (4.25)