Hydrogen atom orbital projections resemble to some Chladni figures! Mathematical reasoning?

Chladni figures are formed by sprinkling salt on a vertically vibrating membrane, f.e. ![1](https://i.stack.imgur.com/hCoBU.jpg). Some of them are purported to be projections of hydrogen atom orbitals f.e. 1s, 2s, 2p, 3d, e.t.c., f.e. ![3](https://i.stack.imgur.com/iz9Fp.png)


One could bring it down to that the vibration patterns of Chladni figures are, as known, two-dimensional standing waves (this part is well established) and also to that -according to the Copenhagen (Born) interpretation- the hydrogen electron distribution also follows a (three-dimensional) standing wave pattern.


So far, so good, but what about the mathematical reasoning lying behind?


Could we claim that the two-dimensional Schrodinger equation for the hydrogen atom (i.e. the radial associated Laguerre polynomial, Ln) and the Chladni figures equation (i.e. the Bessel function of the first kind, Ja) are linear to each other? Any thoughts on the mathematical reasoning would be highly welcome..


