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The Spin of the Electron

Chapter
Part of the Springer Tracts in Modern Physics book series (STMP, volume 186)

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)

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References

  1. 1.
    A. Messiah, Quantum Mechanics I and II (North-Holland, Amsterdam, 1961)Google Scholar
  2. 2.
    H.A. Bethe, R. Jackiw, Intermediate Quantum Mechanics (Benjamin, New York, 1968)Google Scholar
  3. 3.
    F. Schwabl, Quantum Mechanics (Springer, Berlin, Heidelberg, 1992)Google Scholar
  4. 4.
    F. Schwabl, Advanced Quantum Mechanics (Springer, Berlin, Heidelberg, 1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

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