Angular Momentum Hydrogen Atom Problem: Physically Explained When L=0

[LagrangeEuler]

In quantum mechanics hydrogen atom problem $L=\sqrt{l(l+1)}\hbar$. What that means physically when $L=0$?

 

[hacivat]

L = 0 is only possible when l = 0 which means that the wave function has no angular dependence and spherically symmetric.

 

[hilbert2]

And also for a particle moving in some potential energy other than the hydrogenic $V\propto 1/r$, the energy eigenfunctions with $L=0$ are spherically symmetric. These systems include the 3D harmonic oscillator $V(x,y,z) = C(x^2 + y^2 + z^2 )$ and the spherical potential well where $V(r) = 0$ if $r<R$ and $V(r) = V_0$ when $r\geq R$.