Angles.......like in a triangle........................spin.....................electromagnetic waves.......Joe F was right.................but they do have their limits.........any one part of math will only get u but so far................but b/c of the interconnectedness...............trig sums.........can get u far idneed.......

How many quantum numbers?

Main article: Quantum system

The question of how many quantum numbers are needed to describe any given system has no universal answer. Hence for each system one must find the answer for a full analysis of the system. A quantized system requires at least one quantum number. The dynamics of any quantum system are described by a quantum Hamiltonian, H. There is one quantum number of the system corresponding to the energy, i.e., the eigenvalue of the Hamiltonian. There is also one quantum number for each operator O that commutes with the Hamiltonian. These are all the quantum numbers that the system can have. Note that the operators O defining the quantum numbers should be independent of each other^[why?]. Often, there is more than one way to choose a set of independent operators. Consequently, in different situations different sets of quantum numbers may be used for the description of the same system.

Spatial and angular momentum numbers

Four quantum numbers can describe an electron in an atom completely. As per the following model, these nearly-compatible quantum numbers are:

• Principal quantum number (n)
• Azimuthal quantum number (ℓ)
• Magnetic quantum number (m)
• Spin quantum number (s)

The spin-orbital interaction, however, relates these numbers. Thus, a complete description of the system can be given with fewer quantum numbers, if orthogonal choices are made for these basis vectors.