How Does Schrödinger's Wave Equation Describe Quantum Particles?

[el_excellencicc]

..i, am assured this is the right place for this thread -

i, am interested in any arguments [ higher \ otherwise ] anyone may have, of: schroedinger's theory of QM ...in particula his differential QM wave equation, viz: solution Psi[x,t] giving the wave function to be associated with the motion of a particl of mass m under forces described by the potential energy function V[x,t], et cetera ..

..adios..

el_excellencicc

 

[Hyperreality]

Um, I wonder if force can be a well-defined quantity in QM under potentials...

I cannot say I agree with you about the "wave function associated with the motion of particle", rather I think Schrodinger equation smears the image of classical particle and no one really knows about what the wave function $$\Psi(x,t)$$ really is. Till this day, leading physicists admits that they don't exact understand the true nature of quantum mechanics in the documentary "The Elegant Universe".

http://www.pbs.org/wgbh/nova/elegant/program.html"

For me, $$|\Psi(x,t)|^2$$ and $$<\phi|\Psi(x,t)|\phi>$$ seems to have a more "physical meaning" than the wave function itself.

It is important to notice that Schrodinger equation is a non-relativistic equation (Schrodinger tried unsuccessfully to formulate the quantum version). Schrodinger's equation can be deduced through conservation of energy assigning physical quantities to operators (with some ingenuity of course ). We can write Schrodinger equation as simply as

$$H\Psi(x,t)=E\Psi(x,t)$$

The next step towards a realtivistic "equation of motion" for quantum mechanics is the Klein-Gordon equation incoporating Einstein's energy-mass relation.

http://en.wikipedia.org/wiki/Klein-Gordon_equation"

I'm not this advance yet on this issue, but I think that one major flaw of the Klein-Gordon equation is that it does not predict the "spin" of elctrons.
The next step is the Dirac equation.

http://en.wikipedia.org/wiki/Dirac_equation"

Dirac equation not only predicts spins, it also predicts the existence of antiparticle.

 

[el_excellencicc]

schroedinger/Hyperreality

thank you Hyperreality. - have you an argument, for:



http://www.pichotel.com/pic/1750Cz5l5/26452.gif




...giving the total probability of finding somewhere the particl described by the wave function [; the probability must equal one if there is a particl,] ... vis-a-vis: normalisation


...adios

 

[el_excellencicc]

schroedinger's equation

i, think :

http://www.pichotel.com/pic/1750Cz5l5/26475.gif

..may; if, one assumes: schroedinger's equation to be right - is justifiable in QM history ..but: may be bettered, with: algebra and parallelising and apparelment; prehaps .. see the equation with the tautology, of; others !

- substantsively, there is no doubt, of: schroedinger's greatness .


adios

 

[masudr]

the normalisation condition, namely

$$\int^{-\infty}_{\infty} \psi^* \psi dx = 1$$

(at least for square integrable functions defined over [itex][-\infty, \infty][/tex]) is merely saying that the particle must exist somewhere.

Also note that wavefunctions do not only describe particles; they are representations of the state vector in |x> basis.