# How to "read" Schrödinger's equation?

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)

• Do you want to understand the equation? It seems to be quite vague what you are asking:(
– user36790
Commented Oct 6, 2015 at 15:53
• 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.. Commented Oct 6, 2015 at 16:01
• Probably worthwhile reading: physics.stackexchange.com/q/46929 Commented Oct 6, 2015 at 16:03
• 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
Commented Oct 6, 2015 at 16:07
• 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). Commented Oct 6, 2015 at 19:15

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.

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

• I knew you will answer first, as you do always... Thank you, I am reading it now.. Commented Oct 6, 2015 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
Commented Oct 6, 2015 at 16:55
• @Gert: Perhaps the _Pirate_(appropirate) looted the meaning of the sentence!:P
– user36790
Commented Oct 6, 2015 at 17:03
• @user36790: something got looted, for sure.
– Gert
Commented Oct 6, 2015 at 17:07
• @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 Commented Oct 6, 2015 at 18:04