A New Spin on Photoemission Spectroscopy Page: 25 of 259
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(a) z (b) z
2h - - - - - 2(2+)=6h
h h - - - -% +1) =h
x,y -h/2 - Xy
-2h - ----
C= 2 S= 12
Figure 1.1. Schematic of angular momentum vector directions due to space quantization.
(a) The l = 2 case. (b) The s = 1/2 case, an example of the same rules being applied to
intrinsic angular momentum.
of angular momentum along that axis. In this case it is most useful to use equation 1.2
defined along that axis, and by convention it is usually labeled the z-axis. The result of
these rules for a particle with the quantum number l = 2 are diagrammed in Figure 1.1(a).
Equation 1.1 requires the l = 2 state to have an angular momentum vector, L, to have
a length of h6v'. Equation 1.2 requires this vector to be oriented in space such that its
component along the given z-axis can only be -2h, -h, 0, h, or 2h. With this picture we see
that the term "space quantization" does not mean quantizing actual space in this case, but
quantizing the directions L can have in space.
Quantizing angular momentum in a way similar to Equation 1.1 had much experimental
support from agreement between the resulting Bohr model of the atom and studies of
atomic emission spectra which formed discreet lines. Only allowing discreet orientations of
the angular momenta was harder to believe, and many in the early 1920's did not. Most
thought of it as a type of book-keeping which helped explain experiments but should not
be taken literally. This thought is expressed in the autobiography of Max Born: "It took
me quite a time before I took this idea seriously. I thought always that [space] quantization
was a kind of symbolic expression for something which you didn't understand." 3 In 1921,
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Jozwiak, Chris. A New Spin on Photoemission Spectroscopy, thesis or dissertation, December 1, 2008; United States. (https://digital.library.unt.edu/ark:/67531/metadc1014237/m1/25/: accessed April 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.