Course:Physics of Atoms and Molecules/Exercises/Notation
Notation
- L denotes the total orbital angular momentum L = Σ_i l_i , with l_i
single-particle angular momentum. The eigenvalues of L² are such that
L^2|φ>=\hbar ^2L(L+1)|φ> and are simply denoted by the letter L. The
eigenvalues of L_z are such that L_z|φ>=\hbar m_L|φ> and are simply
denoted by the letter m_L
- S denotes the total spin S = Σ_i s_i , with s_i single-particle spin.The
eigenvalues of S² are such that S^2|φ>=\hbar ^2S(S+1)|φ> and are simply
denoted by the letter S. The eigenvalues of S_z are such that
S_z|φ>=\hbar m_S|φ> and are simply denoted by the letter m_S
- J denotes the total angular momentum j_i = l_i+s_i , J = Σ_i j_i.The
eigenvalues of J² are such that J^2|φ>=\hbar ^2J(J+1)|φ> and are simply
denoted by the letter J. The eigenvalues of J_z are such that
J_z|φ>=\hbar m_J|φ> and are simply denoted by the letter m_J
- Keep in mind the addition rules for angular momenta: let us call J₁, J₂
two arbitrary angular momenta. J_{tot}=J₁+J₂ m_{J_{tot}}=m_{J_1}+m_{J_2}
|J_1-J_2|\le J_{tot} \le J_1+J_2 -J_{tot} \le m_{J_{tot}}\le +J_{tot}