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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 ?

Roshan Shrestha
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    Don't conflate the magnetic quantum number $m_l$ (-l to +l) with the spin quantum number $m_s$ (-1/2 or +1/2). – Gert Sep 11 '15 at 00:56
  • You might want to look at https://physics.stackexchange.com/questions/177603/atomic-physics-determining-levels-and-terms --- and as a general point if you have angular quantum number $x$ then the degeneracy of $x$ is $2x+1$ so with $l$ we have $2l+1$ states which are degenerate - at the same energy - until a magnetic field (or electric field splits them) - into $2l+1$ different states.... -- Finally your question is so short it will be closed I'm afraid - but feel free to ask more - just put some more detail in of what you know already and context etc. – tom Apr 10 '18 at 10:57

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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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