Quantum Physics For Dummies
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In analogy with orbital angular momentum, you can assume that m (the z-axis component of spin) can take the values –s, –s + 1, ..., s – 1, and s, where s is the total spin quantum number. For electrons, physicists Otto Stern and Walther Gerlach observed two spots, so you have 2s + 1 = 2, which means that s = 1/2. And therefore, m can be +1/2 or –1/2. So here are the possible eigenstates for electrons in terms of spin:


So do all subatomic particles have s = 1/2? Nope. Here are their options:

  • Fermions. In physics, particles with half-integer spin are called fermions. They include electrons, protons, neutrons, and so on, even quarks. For example, electrons, protons, and neutrons have spin s = 1/2, and delta particles have s = 3/2.

  • Bosons. Particles with integer spin are called bosons. They include photons, pi mesons, and so on; even the postulated particles involved with the force of gravity, gravitons, are supposed to have integer spin. For example, pi mesons have spin s = 0, photons have s = 1, and so forth.

So for electrons, the spin eigenstates are


For photons, the eigenstates are |1, 1 >, |1, 0 >, and |1, –1 >.

Therefore, the possible eigenstates depend on the particle you’re working with.

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Steven Holzner is an award-winning author of technical and science books (like Physics For Dummies and Differential Equations For Dummies). He graduated from MIT and did his PhD in physics at Cornell University, where he was on the teaching faculty for 10 years. He’s also been on the faculty of MIT. Steve also teaches corporate groups around the country.

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