In this statement from Modern Quantum Mechanics by J.J. Sakurai:
If j is an integer, all m values are integers; if j is a half-integer, all m values are half-integers. The allowed m-values for a given j are m=−j,−j+1,…,j−1,j⏟2j+1 states
It says that m will have a total of 2j+1 states. I do not see this, however. Perhaps it is obvious, but could someone explain or show me why if m goes from −j,…,j it will give 2j+1 number of states?
Answer
The 2j is from the positive and negative j values, and the additional +1 accounts for j=0.
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