tag:blogger.com,1999:blog-833078698953665593.post8648999662849417389..comments2011-11-15T00:23:33.850+01:00Comments on me take on GEOMETRY: spherical harmonics and the 3-sphereThilo SchÃ¶nnemannhttps://plus.google.com/102203506387299966297noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-833078698953665593.post-36291036421421685452011-11-15T00:23:33.850+01:002011-11-15T00:23:33.850+01:00The electron, as viewed in the Bohr-Model, is afte...The electron, as viewed in the Bohr-Model, is after all a consequence of the framework of quantum mechanics. It predicts a kind of standing wave, but not only in space, as Bohr's postulates state, but also in time. It's stationary. Tomorrow, if surrounding parameters are untouched, it'll do the same thing as today. <br />This is, what gives rise to the spherical harmonics. They are the mathematical solution to an equation which does not change time (the stationary Schroedinger-equation). This demands symmetry in time. <br />In the case of a hydrogen atom, the only case where spherical harmonics are actually a solution, the equation can be symmetrized even more. It's completly symmetric in all spatial dimensions.<br />So it seems like we need a solution which is symmetrical not only in time or space alone, but in both, and thats where the spherical harmonics comes in. They are the mathematical objects with the desired properties: 4-Dimensional Symmetry (don't know if there a other, would be an interesting question).<br />Time, well, is another thing in quantum mechanics... :)razielhttp://www.blogger.com/profile/11900094364352331062noreply@blogger.com