The Picture Book of Quantum Mechanics by Siegmund Brandt & Hans Dieter Dahmen

Author:Siegmund Brandt & Hans Dieter Dahmen
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

The probabilities fulfill the normalization condition

As an example, we consider the wave packet shown in Figure 10.17a. Its center moves with constant velocity in the negative x direction keeping a constant distance b from the x axis. That is, it behaves like a classical particle with time-dependent position vector

Fig. 10.17(a) The probability ellipsoid, here a sphere, of a free wave packet moving in the x, y plane antiparallel to the x axis, shown at two moments of time. The dispersion of the wave packet is apparent through the growth of the sphere with time. (b) Decomposition of the wave packet shown in part a into angular-momentum states. The height of the column drawn at point (,m) is proportional to the probability that the particle, which is described by the wave packet, has angular-momentum quantum number and quantum number m for the component of angular momentum along the quantization axis n. In this figure n was chosen to be the z axis. Also shown, on the upper margin, are the probabilities _, that the particle possesses quantum number irrespective of the value of m.

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