RE: Schrödinger, the inventor of the master equation of quantum mechanics
Nice post!
Have you used the equation ? i think much of the problems with it gets really clear when you start modelling. Even then 1D and 2D models of THE wave equations use theoretical boundaries like a wall of infinite difference in potency. This when constructed in reality gives rise to i.e QTE, quantum tunnel effect, giving the wave a chance to exist outside the model proving it weak.
When we model carbon chains or chromophores etc we have to add a/2 meaning half a binding length at each end of the molecule for the wave model not to spread beyond the molecule, proving it weak again and hard to use!
All theese applicable models are only build upon classical physics introducing a reoccurring pattern by adding a wave function to solve problems with values in classical models as inputs goes to infinity.
Many of the interesting aspects of the wave equation reveals it self upon usage and many weaknesses.
In short this is just another equation giving rise to different models with more precision but still clear flaws.
Was modelling orbitals and molecules earlier and it got me thinking a bit about this problem, that no physics can prove the existence of anything, only repeat experiments and apply simple models out of repetition. Then new inputs are found proving older models incorrect. Will it ever end := ) ?
Yes I did. I learned Schrodinger equation long ago, taught it more recently, and produce pedagogical material on the topic very very recently ^^
I am not sure to follow the 'flaws' you are mentioning. Do you mind elaborating? However, if you are non relativistic, the only problem is really the Hamiltonian. Once the hamiltonian is settled, the rest follows (assuming we can solve the equation). Getting better and better hamiltonian is somehow a field in itself.
cool its a intresting topic to learn indeed!
The flaws are not in the the wave equation its when applying it to any mechanical model, solving the equation, yes. The model tends to be 100 % precise only in theory, since it requires theoretical limits which we can´t set up in labs giving rise to e.g QET ?
When doing a simple model of a carbon chain molecule in 3D we must add binding lengths which does not exist! only for the electrons not to be partially located outside the molecule we are modelling :) doing this gives the best model of a molecule but its still weak that´s all :)
Thanks. I must admit that I do not know anything about quantum engineering. But from what you say, the problem is not really the equation itself but our failure in managing to correctly model reality. It is probably not trivial (possibly even not possible today) to incorporate all relevant and realistic effects from the perfect world describe by Schrodinger equation. Am I correct?
Yeah exactly.