Undergrad Dimensions of Angular and Radial Nodes

[sams]

Radial and angular nodes are simply a region where the wavefunction is zero. But speaking about their dimensions, do they have any thickness or are they just an infinitesimal point in space without dimensions?

Thanks a lot!

 

[BvU]

They are not points but subspaces. And size zero in math sense. As soon as you give an $\epsilon>0$ for the maximum probability density, that size shoots up to (near?) infinity for all realistic wavefunctions.

 

[sams]

ϵ

What epsilon stands for?

 

[BvU]

A non-zero real number, as in 'for any probability $\epsilon$ > 0 there is a volume > 0 where the wave function is < $\sqrt \epsilon$'

usually $\epsilon$ means very small