The Spin of the Electron

Abstract

Let us introduce the angular momentum operator in the treatment of single particle quantum systems [1, 2, 3,4]. Let us indicate the electron mass by m, the electron position by r, the electron energy by E and the electron momentum by p. In quantum mechanics we assume the following correspondence rules relating the differential operators (Appendix A) and the physical quantities:

$$ \begin{gathered} E \to i\hbar \frac{\partial } {{\partial t}}, \hfill \\ p \to - i\hbar \nabla . \hfill \\ \end{gathered} $$

(1)

Here ħ = h/2π and h = 4.136 × 10⁻¹⁵ eV sec is the Planck constant. The differential operators act on wave functions that are square-integrable complex functions in a Hilbert space. Now, if we consider the components of the electron orbital angular momentum L = r × p, using the definition of L it is possible to see that [L _x ,L _y ]=iħL _z , (2.3) [L _y ,L _z ]=iħL _x ,(2.4) [L _z ,L _x ]=iħL _y .(2.5)