The magnetic orbital quantum number $m_l$ ranges from -l to l, then why $m_l$ has 2l+1 values where l is orbital quantum number ?
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Because the length of the set ${-l,\cdots, l} $ is $2l+1$. It's two times the ${1,\cdots,l}$ plus 1 for the number 0 (which is always included)
Dr Xorile
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