By T. Kuhn
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Additional resources for Black-Body Theory and the Quantum Discontinuity [1894-1912]
Z” represents the finite width of the slit. In our idealized experiment, up to this point, we have been imagining two separate operations to be done on the beam: first, collimation by the wall; second, the measurement done on the beam by the magnets. Let us idealize our experiment even further. Imagine that the action of the thin wall and the beginning of the effect of the magnets on the beam both take place at the same time, or at least approximately simultaneously. Then δz represents an uncertainty in the position of the Ag atoms as they begin their traverse through the magnetic field.
Our conclusion is that electron spin, called “spin 1/2” since Sz = ± /2 only, is a completely nonclassical concept. Its behavior (as in the S–G setup) and its origin (as above) are not accounted for by classical ideas. 5 WAVE FUNCTIONS FOR TWO PHYSICAL-OUTCOME CASE Now let us go back to the S–G experiment again and look at it from a more general coordinate system. Our experimental results from the twomagnet S–G setup are as follows: θ p(+ ,+ ) = cos2 , 2 θ p( −,+ ) = sin 2 . 66) The “+” or “−” are labeling whether the particles are deflected “up” (μz < 0) or “down” (μz > 0), respectively.
145) where n ⋅ σ = n1σ1 + n2 σ2 + n3 σ3 and n is a unit spatial vector n2 = 1. 146) σ1 = σ1 eiφσ3 . 147. Since σ1 and σ3 anticommute, we have, for example, σ 3 σ1 = σ1 ( − σ 3 ) and σ 23 σ1 = σ1 ( − σ3 )2 . Generalizing from these examples, it is easy to see that f (σ3 ) σ1 = σ1 f ( − σ3 ), for f (σ3) any power series function of σ3. We now wish to prove that eiλσ3 eiλ ′ σ3 = ei(λ + λ ′ )σ3 . 149) ⇒ eiλσ3 = cosλ( + + − ) + i( + − − ) sin λ , ⇒e iλσ3 iλ = + e + −e − iλ . 148 above. 146, for example, = σ1eiφ/2 σ3 σ1 = e − iφ σ3 σ1 = e − iφ / 2 σ3 e − iφ/2 σ3 σ1 = e − iφ/2 σ3σ1 eiφ/2 σ3 .