427(2): Comparison of HJ and Schroedinger Equations
Many thanks for checking this note. P is derived from the radial wavefunction R in Eq. (11). Eq. (25) is simply the usual way that the Schroedinger equation is written, and after psi = R sub nl Y sub lm, expands out as you know into the radial R and spherical harmonic Y components of the complete wavefunction psi. This procedure results in Eq. (12), where the angular part enters. |Eq. (26) is simply the Hamilton Jacobi equation from the hamiltonian (25), which is the quantized version of the hamiltonian (1).
427(2): Comparison of HJ and Schroedinger Equations
To: Myron Evans <myronevans123>
It was not explained what the variable bold P is in eq.(12). Shouldn’t a wave function stand there?
In eqs.(25,26) the angular part seems to be missing.
Horst
Am 08.01.2019 um 11:38 schrieb Myron Evans:
427(2): Comparison of HJ and Schroedinger Equations
This note prepares the way for quantization of m theory and a new explanation of the Lamb shift, because the method used in Note 427(1) is the route towards quantization in special relativity first used by Dirac and greatly developed in the UFT series. Quantization of m theory ought to lead to a great deal of new information about atoms and molecules Quantization in a more general space than Minkowski is a clear demonstration of the fact that new energy appears, because in Minkowski space (Dirac theory for example) there is no Lamb shift, contrary to experiment. The Lamb shift is the classic example of the radiative correction due to "the vacuum", which has been developed in recent UFT papers in many complementary ways, all rigorously self consistent.The concept of "vacuum" has also been developed in many different ways throughout the twentieth century. All these theories conserve total energy and momentum, charge current density and so on. The reason for this is that the vacuum is not a "nothingness", it is filled with energy in modern physics.So energy is transferred from the vacuum to matter and total energy is conserved. Anyone who thinks that the Lamb shift is perpetual motion should reexamine their thoughts on physics, or take up gardening. However, in the next note, we will first look firstly at the classical limit of m theory as defined in recent papers UFT415ff, and proceed to quantize that limit on the Schroedinger level. It is anticipated that the wavefunctions and expectation values of the H atom will all be affected by the m(r1) function, and in different ways.