Vector speed projections

FIGURE 2.13 Projections of a vector speeds (cross-section). 

Fig. 12.10. Classical and quantum tops in space, (a) The space is isotropic and therefore the classical top ftteserves its angular momentum i.e.. its axis does not move with respect to distant stars and the top rotates about its axis with a cxxistant speed. This behavior is used in the gyroscopes that help to orient a spaceship with respect to distant stars, (b) The same tc in a homogeneous vector field. The space is no longer isotropic, and therefore the total angular momentum is no longer preserved. The projection of the total momentum on the field direction is still preserved. This is achieved by the precession of the top axis about the direction of the field, (c) A quantum top i.e., an elementary particle with spin quantum number / = in the magnetic field. The projection /- of its spin I is quantized /- =mjH with mj = —, + and, therefore, we have two energy eigenstates that correspond to two precession cones, directed up and down.

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