Learn more. Importance of Schrodinger equation [closed] Ask Question. Asked 6 years, 1 month ago. Active 6 years, 1 month ago. Viewed 4k times. Improve this question. That's pretty important. I study mathematics and I am novice in physics, I just wanted to convince myself of importance of this equation.
Add a comment. Active Oldest Votes. Improve this answer. However, that is not the only place where the electron could be. Learn more about how relativity is misunderstood. Classical mechanics expects an electron to be like a planet orbiting the sun: at a specific radius, with a specific speed. The quantum realm not only explains why the classical view is wrong but also shows how the reality is.
Quantum mechanics here is built around probabilities. The wave function, or psi, is used to calculate these probabilities. However, the tricky point here is to successfully avoid interpreting the quantum realm with classical tools and expectations.
The probabilities of quantum mechanics do not specify where an electron is. What they show is where it is likely to be found. It is a bit complicated but real. According to quantum mechanics, an electron is simultaneously everywhere that the wave function says it is. Learn more about the myths of orbital motion.
In the experiment where one photon and one electron were shot at narrow slits, each acted like particles. Electronic spin must be included in this set of coordinates. The Pauli exclusion principle is a direct result of this antisymmetry principle.
So the Schrodinger equation must be first order in time. One important point that comes out of this is that this means the Schrodinger equation is necessarily a non-relativistic equation, due to the fact that the kinetic energy operator is not first order in space. This derivation has its own importance as it paves the way from classical to quantum mechanics. Such an equation, where the operator, operating on a function, produces a constant times the function, is called an eigenvalue equation.
The function is called an eigenfunction, and the resulting numerical value is called the eigenvalue. Short Answer. Eigenvectors make understanding linear transformations easy. An eigenvalue is a number, telling you how much variance there is in the data in that direction, in the example above the eigenvalue is a number telling us how spread out the data is on the line. More from Other Physics Topics. Use this form if you have come across a typo, inaccuracy or would like to send an edit request for the content on this page.
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By using our site, you acknowledge that you have read and understand our Privacy Policy and Terms of Use. Share Twit Share Email. Home Physics Quantum Physics. Their approach shows that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave. Explore further. More information: Wolfgang P. DOI: This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission.
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