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)