The spin–orbital interaction, however, relates these numbers. As a result of the different basis that may be arbitrarily chosen to form a complete set of commuting operators, different sets of quantum numbers may be used for the description of the same system in different situations.įour quantum numbers can describe an electron in an atom completely:

There is a one-to-one relationship between the quantum numbers and the operators of the CSCO, with each quantum number taking one of the eigenvalues of its corresponding operator.

A complete set of commuting observables (CSCO) that commute with the Hamiltonian characterizes the system with all its quantum numbers. There is also one quantum number for each linearly independent operator O that commutes with the Hamiltonian. There is one quantum number of the system corresponding to the system's energy i.e., one of the eigenvalues of the Hamiltonian. time evolution) of any quantum system are described by a quantum operator in the form of a Hamiltonian, H. A quantized system requires at least one quantum number. Hence these parameters must be found for each system to be analyzed. The tally of quantum numbers varies from system to system and has no universal answer. Any quantum system can have one or more quantum numbers it is thus difficult to list all possible quantum numbers. An important family is flavour quantum numbers – internal quantum numbers which determine the type of a particle and its interactions with other particles through the fundamental forces. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. This distinguishes quantum mechanics from classical mechanics where the values that characterize the system such as mass, charge, or momentum, all range continuously. In particular, this leads to quantum numbers that take values in discrete sets of integers or half-integers although they could approach infinity in some cases. Together, a specification of all of the quantum numbers of a quantum system fully characterize a basis state of the system, and can in principle be measured together.Īn important aspect of quantum mechanics is the quantization of many observable quantities of interest. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian-quantities that can be known with precision at the same time as the system's energy -and their corresponding eigenspaces.

In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system.