Atomic Orbitals & Circular Membranes: Is There a Connection?

[dimensionless]

Is there a particular reason why the probability density distribution function of atomic orbitals bears a similarity to the modes on a circular membrane? Is this just a coincidence? Is it not actually that similar?

 

[lalbatros]

This is a direct consequence of the wave-like behaviour of electrons.
Because of this, the stationary states are normal modes (of the hamiltonian).

 

[ZapperZ]

Is there a particular reason why the probability density distribution function of atomic orbitals bears a similarity to the modes on a circular membrane? Is this just a coincidence? Is it not actually that similar?

It is not "similar" simply because a circular membrane is 2D. You have to solve a 3D equation for atomic wavefunction. Now, the spherical Bessel function that one obtains for the Radial part may have the similar profile with the circular Bessel function that one gets in 2D. But that is as far as it goes. It doesn't have the equivalent of the Spherical Harmonics of the 3D solution.

Zz.