Angular Momentum and Quantization of Measurements

Thus minimizing the total energy (potential plus kinetic) involves a tradeoff. Below a certain separation, the total energy must start to increase with further size reductions the kinetic energy will increase more than the potential energy will decrease. 

Rather than detail these effects here, however, we can illustrate the effects of angular momentum in a simpler case by examining the electronic spin angular momentum S. Experimentally, it is found that all electrons have angular momentum, and the length of the angular momentum vector is always S = a/37 /2. This angular momentum 

Assume the particle is placed into an external magnetic field pointing along the z-direction (B = Bfz). The potential energy for a magnetic dipole in such a field is  

Thus electrons can be deflected by a nonuniform magnetic field (clBtfdz f 0). The force, hence the amount of the deflection, is proportional to the component Sz of the dipole moment along that axis. 

The state Sz = +h/2 is commonly called the spin-up state and Sz = —h/2 is called the spin-down state, but they do not correspond to the angular momentum vec- 

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