Quantum Chemistry 7.6 - Hydrogen Atom Eigenvalues

Short lecture on hydrogen atomic orbital eigenvalues.

The hydrogen atom atomic orbitals have three quantum numbers, n, l, and m which identify each unique orbital. The value of n determines the energy and degeneracy of each shell. The value of l determines the orbital angular momentum (s, p, d, etc). The value of m determines the z-component of angular momentum.

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[TMPChem]

Notes and Corrections:

0:01 The range of allowed values for quantum number l (left side, bottom, purple) should go from zero to n-1, not zero to n as written. Expression should read [ 0 <= l <= n - 1 ].

[jacobvandijk]

Hello. I have a related question. Like you wrote: l = n - 1. This means that l = 0 when n = 1.
Because L = h-bar . [ l . (l+1) ]^0.5 we see that L = 0 too. An electron without angular momentum?
Is that possible? Or am I drawing the wrong conclusion? Hope you can answer this. Thanks a lot!

[solsticetwo]

I can find sense to parametrize solutions in term of energy; but why in term of L or Lz? Why do L and Lz matter?
Also, since they matter, why do not plot L or Lz in the Y-axis as well? If so, ones could note degeneracy for each value of L and Lz

[ernestawoonor-williams]

Shoudn't the angular momentum quantum number, l, go from 0, 1, 2, ..., (n-1)?
That is 0 <= l <= n-1

[aymaneelboujnani]

Is the sin(phi), before the 2nd derivative with respect to phi, squared or it's and error? Because regarding the Rotation Operators video, it is not squared.

Thanks in advance!

[jonathanyara]

you say at around 1:32 that it is d, d theta do u mean partial derivative theta because they dont look like ds

[solsticetwo]

So, H commutes with L^2 and Lz?
What about Lx and Ly?