Linear momentum probability distribution

FIGURE 14.6 Log-normal probability size distributions, illustrating geometrical transposition between number, mass, and linear momentum curves and the mean size particle d,, which can be used in estimating the free-falling velocity of the particle group. 

It should however be noted that the eigenfunctions of the hamiltonian are not eigenfunctions of the linear momentum operator. Accordingly, a measurement of the momentum does not lead to p = 2mE , but to a probability distribution as shown in Fig. 2.3 (refs. 18 and 19). It can be noted that the most probable momentum is not p , when the particle is in a state except when n becomes large. Then the quantum and classical descriptions are similar. 

Fig. 2.3 Probability distribution of the linear momentum p for a particle in a one-dimensional box. (Adapted with permission from the Journal of Chemical Education, 72, 148 (1995) copyright 1995, EMvision of Chemical Education Inc., ref. 18.)...

Fig. 2.2. Isometric projections of probability density pb(0,

Figure 5. a — angular momentum alignment (angular momentum si>atial distribution probability density) created by an absorption of linear polarized light on a Q type of molecular transition and b — angular momentum orientation created by a left-hand polarized light on a P type of moleculctr transition. 

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