Quantum number

A quantum number is any one of a set of numbers used to specify the full quantum state of any system in quantum mechanics. Each quantum number specifies the value of a conserved quantity in the dynamics of the quantum system. Since any quantum system can have one or more quantum numbers, it is a futile job to list all possible quantum numbers. This article therefore illustrates the concepts by choosing two well-known examples, after a brief introduction to the general concept of quantum numbers.

How many quantum numbers?

How many quantum numbers are needed to describe any given system? There is no universal answer, although for each system, one must find the answer for a full analysis of the system. The dynamics of any quantum system is described by a quantum Hamiltonian, H. There is one quantum number of the system corresponding to the energy, ie, the eigenvalue of the Hamiltonian. There is also one quantum number for each operator, O, which commutes with the Hamiltonian (ie, satisfies the relation OH = HO). These are all the quantum numbers that the system can have. In various fields of study, there may be slightly different conventions for writing the quantum numbers, although they can all be related to the definition given here.

Related Topics:
Hamiltonian - Eigenvalue

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