It is suggested that the general form of the constant of quantization, K in Schrödinger's equation, is not h/2π, but K=2sα -k, with s being the spin of the orbiting object, α the fine structure constant (1/137.0361), and k a small positive integer, or zero. For atoms k = 0; for planets and satellites k = 2, 3 or 4; for the solar system as a whole, revolving around the center of the Galaxy, k = 6. The probability that 16 objects of the solar system would follow this quantum rule by chance alone is 1 in 1016, suggestive that quantum mechanics, as we know it today, can be seen as a special case of a more general quantum mechanics of the future; it also supports the view expressed by Dirac, that h is probably not a fundamental constant.
Section 1 contains the basic idea which induced me to undertake an investigation of a relationship between rotational and orbital angular momenta of planets; Sections 2–7 contain the experimental data, the application of the new quantum rule and the statistical evaluation whether the relationship proposed in Section 1, could have occurred by chance alone. The results obtained in Sections 2–7 are noteworthy in themselves, independently whether the basic idea is accepted or not.