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I am starting to learn quantum mechanics. I can't wait for my completion of QM, as I am running behind all the concepts taught in the class; but I can't even go on studying chemistry, or I can't even analyse anything, without understanding the atoms in reality. I believe in (Russell's??) principle of reading equations by converting math-symbolic statements into English statements, and also in Feynman's principle of reading equations by comparing with reality. To be clear on what help I want in Schrödinger's equation, read these statements by Feynman (you may also enjoy reading Russell if interested):

...I have the specific, physical example of what he's trying to analyze [from math equation], and I know from instinct and experience the properties of the thing...

So, I want to understand atoms, their reality, for that I want to read this (Schrödinger's) equation by comparing with physical real atom and knowing each term with the reality, viz. converting the equation completely into plain English without any technical words...
$$i \hbar \frac{\partial}{\partial t}\psi(\mathbf{r},t) = -\frac{\hbar^2}{2m}\frac{\partial^2\psi}{\partial x^2}+V\psi$$

I will be happy if you all can also suggest me books or papers with respect to this matter.

Edits

From Comments: Is it possible to explain that equation with the physical example of an atom with proton and electron, and comparing those terms to what they refer in reality? For example, the differentials may mean certain space of atom, etc.

Related thoughts from my rough book: If every thought represents objects and their conformations in reality (including that of human's inner conformational experience like belief, sadness, or senses), then every thought even that of Quantum Mechanics seems to be able to stand independent of any other previous ones which lead to it, thus may be self contained. (27/07/2016)

If every thought is self-contained I.e. if they can stand independently, can they be arrived without any proto-stages from which they had evolved, provided the fresher is given with all the reality situation with objects representing the conformations presented in the statement? For example, can a fresher directly arrive at the equation $E = mc^2$ with the context, if all the objects involved in the context and equation is confronted by the subject without any knowledge of the evolutionary stages involved in the original production of the same equation and context? (27/06/2016)

Sensebe
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    Do you want to understand the equation? It seems to be quite vague what you are asking:( –  Oct 06 '15 at 15:53
  • Yeah, I want to understand this equation. – Sensebe Oct 06 '15 at 15:54
  • Then read http://www.feynmanlectures.caltech.edu/III_16.html#Ch16-S5; it is really for us :) –  Oct 06 '15 at 15:56
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    Is it possible to explain that equation with the physical example of an atom with proton and electron, and comparing those terms to what they refer in reality? This helps me to satisfy myself now to read other subjects like chemistry, etc, before I understand QM completely.. – Sensebe Oct 06 '15 at 16:01
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    Probably worthwhile reading: http://physics.stackexchange.com/q/46929 – Kyle Kanos Oct 06 '15 at 16:03
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    well you probably could but to me it seems a bit far-fetched to try and relate it to "instinct and experience". Unless you have a very specific experience (or care about subtle details) your world is macroscopic and well described by classical (non-quantum) physics. So maybe you should try to work yourself through the history physics to a point where your "non-quantum" knowledge fails you. I think that might facilitate your understanding of schrödinger's equation. – Bort Oct 06 '15 at 16:07
  • @KyleKanos: Thank your for the reply; Yeah, I saw that before, but it is different. I want these equations to be converted into plain english i.e with no technical words, which describes the real atom... – Sensebe Oct 06 '15 at 16:13
  • @Feynman: I never said it was the same as this one, just that it might be worthwhile to read it. – Kyle Kanos Oct 06 '15 at 16:16
  • @KyleKanos: Sorry, I didn't mean to say that...Sorry, if I gave wrong meaning. I want you to help, don't leave okay.. – Sensebe Oct 06 '15 at 16:19
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    Here's an attempt: The time development of a system depends on the energy of the system. The energy of the system depends on the spatial constraints of the system. – Bill N Oct 06 '15 at 16:24
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    It's possibly worth bringing up the old saw that "no one understands {thing in modern physics}, they just get used to it." (which apparently we stole from von Neumann who first said it about mathematics). – dmckee --- ex-moderator kitten Oct 06 '15 at 19:15
  • Now, I have also asked this question here, to get more help. – Sensebe Oct 07 '15 at 02:02

1 Answers1

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The Schrodinger equation plays the role of Newton's laws and conservation of energy in classical mechanics - i.e., it predicts the future behavior of a dynamic system. It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome. The detailed outcome is not strictly determined, but given a large number of events, the Schrodinger equation will predict the distribution of results.

shrodequat

In the case of an atom that you are talking about you will need the appropirate potential.

anna v
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  • I knew you will answer first, as you do always... Thank you, I am reading it now.. – Sensebe Oct 06 '15 at 16:20
  • "In the case of an atom that you are talking about you will the appropirate potential." Sorry but as a sentence that really doesn't rock. – Gert Oct 06 '15 at 16:55
  • @Gert: Perhaps the Pirate(appropirate) looted the meaning of the sentence!:P –  Oct 06 '15 at 17:03
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    @user36790: something got looted, for sure. – Gert Oct 06 '15 at 17:07
  • So in the picture you linked what is the difference between $H$ and $E$? – Omar Nagib Oct 06 '15 at 17:09
  • In addition to that, the diagram points out the transition from the classical to the quantum mechanical for the left hand side of the equation. What about the right hand side? why is it the case that $E \psi$ Represents the partial time derivative of the wavefunction? – Omar Nagib Oct 06 '15 at 17:13
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    @OmarNagib this is the time independent version of the schrodinger equation. H is the hamiltonian. E is a real number, the eigenvalue of the H operator on psi – anna v Oct 06 '15 at 18:04