Principle Quantum number/Angular momentum/ Magnetic quantum

[Kati Rady-Pentek 1E]

Can someone please explain what the letters n, l, and m represent in a wave function? I'm really confused about what they mean.

[Sohan Talluri 1L]

From my understanding, there are four quantum numbers: principal (n), angular momentum (l), magnetic (m_l), and spin magnetic (m_s). The principal quantum number describes the orbital energy level and size (also called shell). The angular momentum quantum number describes the shape of the orbital (also called subshell), and its allowed values are 0, 1, 2, ... until n-1 (where l=0 corresponds to the s-orbital, l=1 is the p-orbital, l=2 is the d-orbital, and l=3 is the f-orbital). The magnetic quantum number labels different orbitals in the subshell, and has allowed values of l, l-1, l-2 ... until negative l (each number arbitrarily corresponds to an orbital, like p_x, p_y, and p_z). Finally, the spin magnetic quantum number can be either +1/2 or -1/2 and accounts for two paired electrons being in the same orbital.

Hopefully this helps, and please correct me if there are any mistakes.