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- TL;DR Summary
- The electron's wavefunction is usually expressed in the standard basis {n, l, m_l, s, m_s}, but how to express it in the basis {n, l, m_l, s, m_j} ? (Note that m_s is replaced with m_j.) Or is it that certain combinations of quantum numbers are forbidden?
I've seen the hydrogen electron's wavefunction expressed in the basis or , but so far, never in . My question is, are certain combinations of quantum numbers, eg, , forbidden?
If is not forbidden, how do we get it from the standard basis ?
I know how to get from using Clebsch-Gordan coefficients:
where .
is the total angular momentum.
But other than that, I do not know how to express the wavefunction in other bases.
If
I know how to get
where
But other than that, I do not know how to express the wavefunction in other bases.
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