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p q r linear combinations of quantumnumbers 62
rj unit spinor
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analogy antisymmetric calculation complex conjugates conclude considered constants of motion coordinate system corresponding defined depend derived differential operators differential symbols dimensional spinor discussed eigenfunctions eigenvalue electron problem electron spin electron system electrostatic interaction energy levels energy values expression field of force formalism formulae Hamiltonian integrand introduced iSv)k Kramers linear combinations linear transformation linearly independent magnetic field magnetic quantum number matrix elements means of spinor method of spinor momenta monomials normalisation integral obtained occur orbital angular momentum orbital functions Pauli matrices permutations perturbation energy ponents properties of spinor Schrodinger equation solutions spatial coordinates spherical harmonics spin functions spin operators spin quantum spin space spinor components spinor invariants spinor monomials spinor polynomials spinor transformations substituted term containing three dimensional space total angular momentum total orbital angular total spin trans transformation properties unit spinors unitary transformation written yields z-axis