The Statistical Interpretation of Wave Mechanics

We have already mentioned the interpretation of the wave function given by the author (p. 83). Let the proper function corresponding to any state be then dv is the probability that the electron (regarded as a corpuscle) is in the volume element dv. 

This interpretation is almost self-evident, if we consider, not the quantum states proper (with discrete, negative energy-values), but the states of positive energy, which correspond to the hyperbolic orbits of Bohr s theory. We have then to solve a wave equation 

If we extend this statistical interpretation to the case of discontinuous states, and if is the energy and i/ /n the proper function of such a state, then i/j.n is the probability that an electron will be found precisely in the volume ehunent dv this holds in spite of the fact that the experiment if carried out would destroy the connexion with the atom altogether. The probability of finding the 

We speak frequently of a density distribution of the electrons in the atom, or of an electronic cloud round the nucleus. By this we mean the distribution of charge which is obtained when we multiply the probability function /r for a definite state by the charge e of the electron. From the standpoint of the statistical interpretation its meaning is clear it can be represented pictorially in the way shown in fig. 21, Plate VII. The figures represent the projections (shadows) of the electronic clouds in various states the positions of the nodal surfaces can be recognized in them at once. 

From another point of view, the statistical interpretation of wave functions suggests how the radiation emitted by the atom may be calculated on wave-mechanical principles. In the classical theory this radiation is determined by the electric dipole moment p of the atom, or rather by its time-rate of variation. By the correspondence principle, this connexion must continue to subsist in the wave mechanics. Now the dipole moment is easily calculated by wave mechanics if we adhere to the analogy with classical atomic mechanics, it is given by 

---