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aditya23456
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is schrodinger equation capable of explaining all the properties of electron dynamics or are there any anomaly..?
THANKS IN ADVANCE
THANKS IN ADVANCE
For some reason, that relativistic Schrodinger equation is today called Klein-Gordon equation.dextercioby said:Depends on what you mean by Schrödinger's equation. In 1926 he published 2 equations for the electron, one of them took into account the theory of special relativity, while both of them didn't account for the electron's spin angular momentum.
Demystifier said:For some reason, that relativistic Schrodinger equation is today called Klein-Gordon equation.
The relativistic Schrodinger (KG) equation describes the pionic atom very accurately, and measurements of pionic x rays in calcium and titanium were used to determine the mass of the pion. See Robert E. Shafer Phys. Rev. 163, 1451 (1967).M Quack said:That is misleading. The KG equation is relativistic, but describes a spin-zero particle. The electron has spin 1/2 and the relativistic equation to best describe it is the Dirac equation.
Demystifier said:To summarize all this in a confusing way:
...
Further complication arises if you include the insight from string theory, but are you sure that you want to see that too?
Actually, not yet.M Quack said:Now the confusion is complete :-)
Demystifier said:Actually, not yet.
I have further extended it in my blog:
https://www.physicsforums.com/blog.php?b=3873
The best comparison I have seen between the non-relativistic (NR) and relativistic Schrodinger (Klein Gordon, KG) equations is in Schiff "Quantum Mechanics". Chapter II. Eq 6.12 uses E = p^{2}/2m (NR), while in Chapter XII, Eq(42.2) this becomes E^{2} = (pc)^{2} + (mc^{2})^{2} (KG). The hydrogen atom KG atomic energy levels are different, and there is splitting for different orbital angular momentum l (\ell) quantum numbers (not true in NR solution). Compare Eq (16.38A) and (42.21). Both of these differ from the Dirac solution Eq.(42.27).aditya23456 said:I still don't get the point concerning relativistic equation for electron..Why relativistic equation is needed to describe motion of electron..? If electron goes at comparable to light speed Its space and ofcourse time should contract :/ and at the same time it should become massive which is not the case..
PS: I m just learning quantum mechanics and learning in a hurry which may lead to SUPERPOSITION of other concepts...Hope I sound meaningful and please correct me if I m wrong anywhere
The Schrodinger equation is a mathematical equation that describes the behavior of quantum particles, such as electrons, in a given physical environment. It was developed by Austrian physicist Erwin Schrodinger in 1926.
Yes, the Schrodinger equation has been extensively tested and has been found to accurately describe the behavior of electrons and other quantum particles under various conditions.
No, the Schrodinger equation only describes the behavior of electrons in terms of their wave function. It does not provide a complete understanding of the underlying physical properties of electrons, such as their exact position and momentum.
One of the main limitations of the Schrodinger equation is that it does not take into account the effects of relativity. It also does not account for interactions between multiple particles, making it less accurate for systems with more than one particle.
No, there are other equations, such as the Dirac equation, that are used to describe electrons in specific situations. The Schrodinger equation is generally used for non-relativistic systems, while the Dirac equation is used for relativistic systems.