Agreed, the plane in this case is defined by the basic hamiltonian of an assumed planar orbit. More generally the hamiltonian must be expressed in terms of r, phi and theta. I will do this shortly. Planetary orbits are two dimensional but orbitals are three dimensional, or four dimensional in relativistic orbits.
Sent: 29/07/2014 07:47:54 GMT Daylight Time
Subj: Re: Computational results from 267(4): Velocities and Expectation Values of rThis is what happens when we approximate a 3D real world with 2D representations. The same is true in optics using ray diagrams etc. Unfortunately, we tend to see and think in 2D – and lose detail and information as a consequence (as you elegantly show here). Much of physics is still locked in a flat world!
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