Magnetic quantum number

In atomic physics, the magnetic quantum number, designated by the letter m_l, is the third in a set of four quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron. The magnetic quantum number distinguishes the orbitals available within a subshell, and is used to calculate the azimuthal component of the orientation of orbital in space. Electrons in a particular subshell (such as s, p, d, or f) are defined by values of ℓ (0, 1, 2, or 3). The value of m can range from -ℓ to +ℓ, inclusive of zero. Thus the s, p, d, and f subshells contain 1, 3, 5, and 7 orbitals each, with values of m within the ranges ±0, ±1, ±2, ±3 respectively. Each of these orbitals can accommodate up to two electrons (with opposite spins), forming the basis of the periodic table.

There is a set of quantum numbers associated with the energy states of the atom. The four quantum numbers ${\displaystyle n}$, ${\displaystyle \ell }$, ${\displaystyle m}$, and ${\displaystyle s}$ specify the complete and unique quantum state of a single electron in an atom called its wavefunction or orbital. The Schroedinger equation for the wavefunction of an atom with one electron is a separable partial differential equation. (This is not the case for the helium atom or other atoms with mutually interacting electrons, which require more sophisticated methods for solution) This means that the wavefunction as expressed in spherical coordinates can be broken down into the product of three functions of the radius, colatitude (or polar) angle, and azimuth:

...
Wikipedia