Spin - The player's expected winnings is $-0.398
What is Spin?
In addition to composite particles (hadrons) as well as atomic nuclei, elementary particles also carry the conserved quantity known as spin. In quantum mechanics, there are two different types of angular momentum: orbital angular momentum and spin angular momentum. The orbital angular momentum operator, which appears when the wavefunction of an orbit has periodic structure as the angle changes, is the quantum-mechanical equivalent of the classical angular momentum of an orbital revolution. While the polarisation of light has a classical counterpart in photons, the quantum-mechanical equivalent is spin for electrons. Experiments like the Stern-Gerlach experiment, wherein silver atoms were found to have two potential discrete angular momenta despite it having no orbital angular momentum, are used to infer this same existence of electron spin angular momentum.
[tex]\begin{array}{l}\frac{2}{5}(9-4)+\frac{1}{5}\left(\frac{1}{100}-4\right)+\frac{3}{10}(0-4)+\frac{1}{10}(0-4) \\=\frac{2}{5}(5)+\frac{1}{5}\left(\frac{-399}{100}\right)+\frac{3}{10}(-4)+\frac{1}{10}(-4) \\=2-\frac{399}{500}-\frac{12}{10}-\frac{4}{10} \\=2-0.798-1.2-0.4 \\=-0.398\end{array}[/tex]
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