QM really makes me confused. Classical Theories gone wrong in QM.
That is because we believe classical theories were always wrong. People thought the world was flat because thats what you see, until you can circum-navigate it and make other key observations then you realize it isn't flat.
Perception is everything to us and we most easily decieve ourselves.
I want to ask, why phase factor=e^(kx-wt+phi) ? The induction of Schrodinger's equation is easy. but where is this e^(kx-wt+phi) come from?
It comes from the premise that phase space has that there are two and exactly two positions for matter in the universe created by two waves in superposition. Unlike Everetts multiverse where there are many universes phase space has only two so when something is in superposition it is oscillating between them.
Look at the formulation of two standing waves beating against each other (
http://www.kettering.edu/physics/drussell/Demos/superposition/superposition.html)
See superposition is not unique to QM it's a behaviour of any normal waves.
So the derivation of that formula describes two wave spaces in superposition beating against each other.
This one is an overview that is reasonably old it still shows compatability of the theory with other theories like SUSY but it will give you an feel for the subject because it's reasonable simple presentation
http://www.lpt.ens.fr/IMG/pdf/Bars.pdfIt all sounds weird until you realize that you need this sort of mathematics for describing movement in an ocean because you have wind and tide motions which create standing waves.
If you tried to describe motion on an ocean with no global reference, so you are at sea no GPS no sign of land how do you describe your motion? You can only do it realive to things around you like a log on the water etc. But you have a huge problem don't you because you realize that you must be drifting but without reference how do you calculate that, think about what your world looks like.
I am sure sailors who have been lost at sea could describe the world very well for you. See phase space is not so strange if you are far out at sea with no GPS :-)
Momentum is proportional to frequency. p=hf
Can we measure motion which smaller than h-bar? and now, why is h-bar?
You can not measure anything smaller than the smallest beat between the two wave spaces which becomes your plank constants. Thats another strength of the theory it explains why plank distance, plank time etc exist. And that explains your question if you follow the extraction of formulas out.
Phase space is not going to be like string theory hang around for a longtime if it's wrong because it makes alot of predictions it will die very fast if wrong.
