Feb 14 2008

Half-integer spin contribution

Published by at 8:11 pm under Quantum Mechanics

With the emission of a graviton, an electron in an atomic quantum orbit must either undergo a nutation, or reverse its spin orientation as it contributes to the particle angular momentum.
The shape of an orbital that you see at the top of this blog is similar to what many of us picture, however reality may be something different.  Let us say, for discussion purposes, that an electron reverses its spin orientation when it gives off a graviton.  The electron as a particle with half-integer spin changes sign “when the system of coordinates is completely rotated about an axis” ([1], §54).   Should each orbital then include graviton emitting turns of quantity 2n+1, n=1,2,3, the spin orientation of the electron would reverse for every course that brings it back to its orientation and position relative to starting coordinates within d(q-q’).  The total particle angular momentum will then alternate along any prescribed axis between j = l + ½ and j = l – ½.
Another way of stating it is that for half-integer j, Χ(Ф+2π) = – Χ (Ф).  The base function changes sign under a rotation of 2π ([1], §95).
It is the statistical nature of quantum mechanics that has allowed its angular momentum and energy eigenvalue determinations to be very useful in physics.  The average intrinsic spin angular momentum of the electron has thus been able to be used without respect to the emission and absorption of gravitons.

[1] Landau, L. D. and Lifshitz, E. M., Quantum Mechanics, Non-relativistic Theory, Translated from the Russian by J. B. Sykes and J. S. Bell, Addison-Wesley Publishing, 1958

One response so far

One Response to “Half-integer spin contribution”

  1. Kevinon 16 Apr 2008 at 7:52 pm

    It appears that the highest principal quantum number is 7, as in uranium, so the highest number of turns in an orbital would be 15.

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