# Why are quantum numbers assigned to electrons?

Specifically the principal quantum number ($$n$$), orbital quantum number ($$l$$) and orbital magnetic quantum number ($$m_{l}$$). For systems like the hydrogen atom, these quantum numbers arise from the Schrödinger equation which involves:

• A potential energy function, for the system of the electron and the nucleus
• A wave function, also characteristic of the same system, determined by the electron and it's interaction with it's environment

Wouldn't it then be more appropriate to assign quantum numbers to the electron-nucleus system rather than the electron itself?

Several sources always describe the quantum numbers (particularly in multi-electron systems) to be a characteristic of an electron, including the exclusion principle, so I am unsure if my reasoning is correct.

Here's the paragraph from the Wikipedia page on the exclusion principle:

it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: n, the principal quantum number; ℓ, the azimuthal quantum number; $$m_ℓ$$, the magnetic quantum number; and $$m_s$$, the spin quantum number.

• Yes, the quantum numbers belong to the atom as a whole. If a source tells you they belong to the electron(s), they are being imprecise (either deliberately, to simplify things, or because they don't know better).
– d_b
Jan 29 at 5:39
• As @d_b says. I would add that it is a left over of the Bohr model, which has been superseded by the Schrodinger solutions but is still useful where its solutions and the strict quantum solutions coincide. Jan 29 at 5:59