1. Indistinguishable Particles  A (r),  B (r): Two identical particles A and B in a certain states r Since the particles are indistinguishable, this requires: |  (r 1,r 2 )| 2 = |  (r 2,r 1 )| 2 Searching for a wave function  that describes both particles being in states r 1 and r 2  (r 1,r 2 ) =  (r 2,r 1 ) or  (r 1,r 2 ) = –  (r 2,r 1 )  S (r 1,r 2 ) = 1/  2 [  A (r 1 )  B (r 2 ) +  B (r 1 )  A (r 2 )] - Bosons  A (r 1,r 2 ) = 1/  2 [  A (r 1 )  B (r 2 ) –  B (r 1 )  A (r 2 )] - Fermions Two particles in the same state (r 1 = r 2 ):  S (r 1,r 1 ) = 1/  2 [  A (r 1 )  B (r 1 )+  B (r 1 )  A (r 1 )] = 1/  2 ∙ 2  A (r 1 )  B (r 1 ) =  2  A (r 1 )  B (r 1 )  |  S (r 1,r 1 )| 2 = 2 |  A (r 1 )| 2 |  B (r 1 )| 2  A (r 1,r 1 ) = 1/  2 [  A (r 1 )  B (r 1 ) –  B (r 1 )  A (r 1 )] = 0  |  S (r 1,r 1 )| 2 = 0 Bose-Einstein condensation Pauli-exclusion principle

2. Spinning Electron – Magnetic Dipole B L B L - N S

3. Stern-Gerlach Experiment S N S N N S S N S N S z = ↑ S z = ↓ S y = ←/→ S z = ↑ S y = →

4. Understanding the Spin N S B F F r r  torque: M = 2 r × F - L M = dL/dt (analogue to F = dp/dt) M M S z well defined S x, S y changing

5. S N S N N S S N S N S z = + ½ ħ S z = – ½ ħ S z = + ½ ħ S y = + ½ ħ - S S - - Stern-Gerlach Experiment