"Where did we get that (equation) from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger." ---Richard Feynman
Today I dusted the physics shelf at the local university. Read a physics text from the 70s. The author unwittingly proposed a twined configuration to solve the wavefunction part of Schrodinger's steady-state equation for 3D. Of course he failed to realize the implications. Thank God we have brilliant physics professors who write shelves full of books!!!
Excerpt from Modern Concepts in Physics by Beiser
In general, Schrodinger’s steady state equation can be solved only for certain values of the energy E. What is meant by this statement has nothing to do with any mathematical difficulties that may be present, but is something much more fundamental. To “solve” Schrodinger’s equation for a given system means to obtain a wave function that not only obeys the equation and whatever boundary conditions there are, but also fulfills the requirements for an acceptable wave function---namely, that it and its derivatives be continuous, finite, and single-valued. If there is no such wave function, the system cannot exist in a steady state. Thus energy quantization appears in wave mechanics as a natural element of the theory, and energy quantization in the physical world is revealed as a universal phenomenon characteristic of all stable systems.
A familiar and quite close analogy to the manner in which energy quantization occurs in solutions of Schrodinger’s equation is with standing wave in a stretched string of length L that is fixed at both ends. Here, instead of a single wave propagating indefinitely in one direction, waves are traveling in both the + x and –x directions [bidirectional, diametrical] simultaneously subject to the condition that the displacement y always be zero at both ends of the string [Mossbauer's recoilless emission]. An acceptable function y(x,t) for the displacement must, with its derivatives, obey the same requirements of continuity, finiteness, and single-valuedness as sigma and, in addition, must be real since y represents a directly measurable quantity. (p. 147, 148)
Beiser says "familiar and close analogy" because his supposition is that the mediator of light is a discrete force-carrying particle-wave. How discrete particles wave is beyond me. And what connects all these discrete particles??? Mystical forces??? Physics is not theology or an episode of ghost hunters. Do bullets bloody wave? Do particles perform miracles like carry force (push, pull)???
Here is a copy of his figure. I filled in the dots for him. He had one of the 'strings' dotted!!!
A rope like configuration is the only real 'solution' to this part of Schrodinger's equation. Only a twined configuration can meet the required prediction of a standing wave in stationary state.
Now suppose that this continuous and finite twined entity represents the architecture of light. Suppose that in reality it is comprised of an Electric Thread and a Magnetic Thread through which all the Hydrogen atoms of the Universe are connected, and not only that, suppose that gazillions of these configurations converge and bifurcate to form the Hydrogen atoms and all heavier elements produced from hydrogen. Suppose that when all the atoms quantum jump they torque various light signals, to and from each other via these rope like entities (each twist signal represents Schrodinger's energy quanta). Suppose also that the constant torquing creates tension throughout the network and that this taut rope like entity mediates gravitational attraction. Well then particle physics, quantum mechanics, General and Special Relativity, Big-Bang, Strings, etc. would all be in vain.
And that is the long and short of it. The followers of these disciplines have esoteric equations, billion dollar labs/toys, a host of measurements, power, influence, etc. but they cannot make manifest to you the architecture and mechanics of light or what causes an apple to fall to the ground, or what neutrinos are, or how magnets attract and repel, etc.