4 ms·

Isn’t this a good model for the hydrogen atom? But then not for other elements?

• alecst 4y ago
  If a quantum system is spherically symmetric, like the hydrogen atom is, then its energy states are gonna correspond to certain groups of spherical harmonics. That's why they're used when you study the hydrogen atom. This comes out of a branch of math called representation theory.
• drowsspa 4y ago
  There's always perturbation theory for that
• jameshart 4y ago
  Spherical harmonics are a good model for any spherical density function. You could describe the electron probability densities of a particular energy level of any atom in terms of spherical harmonic coefficients. I think it just happens that hydrogen atoms electron clouds have particularly simple sets of coefficients so their density functions look a lot like the raw harmonic bases. That’s more because hydrogen atoms are simple than because of anything profound. Like, when something vibrates in 1D, if it’s simple (like a mass on a spring) it will move in a simple sine wave - the Fourier coefficients describing its behavior will be simple, because it is simple. But if it’s more complicated (like, a lump of jelly on a linked set of springs) it will move in a complex wave, with complex Fourier coefficients. Its behavior will be complex because it is complex. That hydrogen electron clouds look like these lobed shapes then is as unsurprising - or possibly as surprising, depending how you feel about the unreasonable power of mathematics I guess - as the fact that a weight on a spring follows a sine wave.
  • alecst 4y ago
    It has to do with representations and quantum mechanics. The energy eigenvalues of the hydrogen atom are tied to L values of the spherical harmonics.