iħ ∂/∂t Ψ(r,t) = [-ħ2/2m∇2+ V(r,t)]Ψ(r,t)
Where did we get that equation from? Nowhere. It is not possible to derive it from anything that you know. It came out of the mind of Schrödinger
– Richard Feynman
This equation is one of the cornerstones of modern physics and is how physicists go about describing reality. It outlines how the quantum state of some particular system changes with time. It is the fundamental theoretical quantity in quantum mechanics; one of the founding postulates in fact. The wave function is a mathematical construct that depicts all of the possibilities that can happen to any given system. All of them, no matter how outlandish or unlikely; it will describe them all. It is the most complete description that can be given to a physical system.
This particular function is defined and calculated by the Schrödinger Wave Equation. In its simplest interpretation it provides a probability distribution of finding a single particle in a given position, but by extension can be expanded to accommodate the entire universe. It gives us a physical description of everything that could possibly happen to something once we observe it.
However in our everyday ‘reality’ we usually only ever see one version of something, not an endless proliferation of possibilities like cats that are both alive and dead at the same time. This is because at the very instant that we make an observation or measurement, the wave function collapses leaving only what actually coalesces into our reality. In essence one could look at this as though we are constantly creating our own realities because of our observations. We make the universe so because we observe it to be so. Now this doesn’t imply that we can somehow influence what the wave function collapses into. That is a random event. It can be predicted using probabilities, but that is another story. All we do is influence when the wave function collapses.
There is no way to actually prove that Schrödinger’s equation is true, other than testing its predictions experientially; which of course has been done successfully for almost 90 years now.
When the chi condenses, its visibility becomes apparent so that there are then the shapes of individual things. When it disperses, its visibility is no longer apparent and there are no shapes.
-Zhang Zai