Angular Momentum II Using Bra and Ket Algebra

Abstract

In Chapter 9 we had introduced the quantum mechanical angular momentum operator L and had shown that its components satisfy the following commutation relations:

$$ \left. {\begin{array}{*{20}{c}}{\left[ {{L_x},{L_y}} \right] = i\hbar {L_z}} \\{\left[ {{L_y},{L_z}} \right] = i\hbar {L_x}} \\{\left[ {{L_z},{L_z}} \right] = i\hbar {L_y}} \\\end{array}} \right\} $$

((1))

We had also shown that the square of the angular momentum operator L ² (≡ L ² _x + L ² _y + L ² _z )commutes with L _x , L _y and L _z ; i.e.

In a one-page letter to the Editor of Naturwissenschaften dated 17 October 1925, Samuel A. Goudsmit and I proposed the idea that each electron rotates with an angular momentum ħ/2 and carries, besides its charge e, a magnetic moment equal to one Bohr magneton¹, e ħ/2mc...

George E. Uhlenbeck in Fifty Years of Spin: Personal Reminiscences, Physics Today, p. 43, June 1976.