Hydrogen Atom orbital and quantum number

[terp.asessed]

I am wondering and have been thinking, exactly how does the energies of hydrogen atom orbital depend on quantum numbers? I am just curious because all of what I have learned/read discusses only one-dimensional situaiton, like a particle in a box, and I want to know how it can be applied to the 3D case of hydrogen atom...is it simply application of x and y and z boxes? I am also curious if Hamiltonian operator is applicable to Hydrogen atom too?

 

[Nugatory]

Yes, Schrödinger's equation $H\Psi=E\Psi$ still applies in this case, where H is the Hamiltonian. $\Psi$ isn't just a function of $x$ though; in the three-dimensional case it's a function of x, y, and z (although in the electron orbital case it's easier to use polar coordinates, and that's what everyone uses for this problem).

Google for "hydrogen atom Schrödinger equation" and you'll find the solution for the hydrogen atom, orbitals and all.

 

[Khashishi]

The hydrogen atom obeys the same principles as the particle in a box, but there is a potential well instead of a box.
It might behoove you to study the case of the 3D quantum harmonic oscillator, which is intermediate in progress between the particle in a box and the hydrogen atom. It's almost the same as the hydrogen atom, but can be done in rectangular coordinates as well as polar coordinates.

 

[terp.asessed]

Thank you very much! I will check out both 3D Schrödinger Eq. and harmonic oscillation.