Schroedinger to another level

  • Thread starter el_excellencicc
  • Start date
In summary: In that sense, it is not appropriate to say that "the wave function is associated with the motion of particle"; rather, it is associated with the state of the system. This is an important distinction in understanding the true nature of quantum mechanics.In summary, the conversation revolves around Schrodinger's theory of quantum mechanics, specifically his differential wave equation and its solution. There is a disagreement about the concept of force in QM and the true nature of the wave function. The conversation also touches on the development of the Klein-Gordon and Dirac equations and their predictions. The purpose of the conversation is to discuss the normalisation condition and its justification in QM. Overall, there is admiration for Schrodinger's contributions to the field, but
  • #1
el_excellencicc
3
0
..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
 
Physics news on Phys.org
  • #2
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 [tex]\Psi(x,t)[/tex] 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, [tex]|\Psi(x,t)|^2[/tex] and [tex]<\phi|\Psi(x,t)|\phi>[/tex] 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:rolleyes: ). We can write Schrodinger equation as simply as

[tex]H\Psi(x,t)=E\Psi(x,t)[/tex]

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" [Broken]

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" [Broken]

Dirac equation not only predicts spins, it also predicts the existence of antiparticle.
 
Last edited by a moderator:
  • #3
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
 
Last edited:
  • #4
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
 
  • #5
the normalisation condition, namely

[tex]\int^{-\infty}_{\infty} \psi^* \psi dx = 1[/tex]

(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.
 
Last edited:

1. What is the concept of "Schroedinger to another level"?

The concept of "Schroedinger to another level" refers to the application of the principles of quantum mechanics, specifically the Schrödinger equation, to larger and more complex systems. This allows for a better understanding of the behavior and properties of these systems, which cannot be fully explained by classical physics.

2. How is "Schroedinger to another level" different from traditional quantum mechanics?

"Schroedinger to another level" goes beyond traditional quantum mechanics by considering the interactions and behaviors of multiple particles or systems, rather than just a single particle. It also takes into account the effects of entanglement and superposition on these larger systems.

3. What are some potential applications of "Schroedinger to another level"?

Some potential applications of "Schroedinger to another level" include understanding and predicting the behavior of complex molecules and chemical reactions, developing more efficient and powerful quantum computers, and studying the properties of materials at the nanoscale.

4. What are the challenges involved in studying "Schroedinger to another level"?

One of the main challenges in studying "Schroedinger to another level" is the complexity of the mathematical equations and calculations involved. It also requires advanced technology and techniques to manipulate and observe these larger quantum systems.

5. How does "Schroedinger to another level" contribute to our understanding of the universe?

"Schroedinger to another level" allows us to better understand the fundamental principles that govern the behavior and interactions of matter at a microscopic level. This can help us gain insights into the workings of the universe and potentially lead to new discoveries and advancements in various fields of science and technology.

Similar threads

Replies
17
Views
1K
  • Quantum Physics
Replies
5
Views
330
  • Quantum Physics
2
Replies
36
Views
1K
Replies
9
Views
1K
  • Quantum Physics
Replies
1
Views
1K
Replies
1
Views
701
Replies
41
Views
4K
  • Quantum Physics
Replies
31
Views
2K
Replies
1
Views
484
Replies
1
Views
542
Back
Top