This is a simple illustration of an energy shift caused by m space, in the non relativistic limit of the free particle Schroedinger equation. In the usual space the equation produces the result (6), the quantized energy levels of the free particle. Then use the invariance of phase under frame transformation to show that the wavefunction is invariant. Finally the energy levels in m space of the free particle are given by Eq. (12). There is an energy shift caused by the m space itself. One can go through all the well known problems of elementary quantum mechanics in this way: particle in a box, quantum tunnelling, particle on a ring and sphere, and the H atom.

a435thpapernotes4.pdf

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