Physics Lecture 19

# Physics Lecture 19 - Lecture 19: Spin, Multiple Particles,...

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Lecture 19: Spin, Multiple Particles, Atoms & Lasers I. Spin A. Intrinsic angular momentum 1. Particles act as if they are spinning 2. Concept Test: if momentum is in z direction, there is no angular momentum in the x direction (Classically) B. Experimental Observations 1. Magnitude of intrinsic angular momentum is constant 2. Spin can be non-zero for particles with no size 3. Only certain values allowed for spin component in a certain direction a. Concept Test: if angular momentum is ħ/2 in the z direction, you will measure either ħ/2 or –ħ/2 in any direction 4. Fermions – S = 1/2, 3/2 5/2 Boson – S = 0, 1, 2, 3 5. Spin up: |+z> = ħ/2 |-z> = - ħ/2 |+x> = sqrt(1/2)|+z> + sqrt(1/2)|-z> |-x> = sqrt(1/2)|+z> - sqrt(1/2)|-z> |+y> = sqrt(1/2)|+z> + i* sqrt(1/2)|-z> |-y> = sqrt(1/2)|+z> - i* sqrt(1/2)|-z> 6. Example: |<-y|+x>| 2 = |(sqrt(1/2)<+z| + i* sqrt(1/2)<-z|)| (sqrt(1/2)|+z> + sqrt(1/2)|-z>)| = |1/2 – i 1/2| 2 = ¼ |1- i | 2 = ¼ (1- i )(1+ i ) = ½ II.

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## Physics Lecture 19 - Lecture 19: Spin, Multiple Particles,...

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