Sunday, January 11, 2009
What are GOOD QUANTUM NUMBERS?
In classical mechanics, we can assign any number of variables to specify the state of a system. For example, for a free particle, its position, momentum, etc,. can be known and can be assigned simultaneously to specify the state of the free particle. But the story of quantum mechanics is different. If the position of a particle at some instant is correctly known, its momentum will be highly/maximally uncertain. This means, we can't assign both the position and momentum to specify the quantum mechanical state of the particle simultaneously. In this sense, the quantities (observables) which can be assigned simultaneously to a quantum system at any time to specify its state at that time are called the good quantum mumbers of the system. A set of good quantum numbers is also called a complete set of commuting observables (C.S.C.O.). These coordiantes commute each other, which means that their measurements can be made simultaneously.