Is there a proof of the time-dependent Schrödinger equation? In many books, we find the proof of the time-independent Schrödinger equation which can be derived from the wave equation and the expression of de Broglie wavelength.  But what about the time-dependent equation? In ion-atom collisions, there is a way to prove the eikonal equation which is similar to the TDSE where the starting point is TISE, if we consider that the projectile ion does linear trajectories, time can be embedded and we prove the eikonal equation that very known in a semiclassical treatment of ion-atom collisions. Is there a similar proof for example, and how time is introduced?
How can one derive Schrödinger equation? The  is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his experiments. My question is, can one derive the Schrödinger equation mathematically?
something like wye-delta and delta-wye connection.  we can originally know wye-delta connection is step-down transformer and second side voltage phase is being to -30 degree. And also delta-wye connection is step-up transformer and second side voltage phase is being to +30 degree.  But the other side, we also can make wye-delta connection is step-up transformer if it get turn ratio like 1:2. So in this case maybe will be become +30 degree in second side voltage.   apply this principle in scott connection, how can work it?   case1) turn ration 1:2 - step up second side voltage's angle +90 degree?  case2) turn ration 2:1 - step down second side voltage's angle -90 degree?  if you have any information or homepage link, can you leave it for me?  thank you so much. Why is inductance (L) proportional with turns-square (N²)? We start from the   $$ \mathbf{\nabla} \times \mathbf{B} = \mu \mathbf{J} + \overbrace{\mu \epsilon \dfrac{\partial \mathbf{E}}{\partial t}}^0. $$  We take surface integration of both sides, for the surface (\$s\$) inside the mean path (\$c\$) of the core.  $$ \int_s \left( \mathbf{\nabla} \times \mathbf{B} \right) \cdot d\mathbf{s} = \mu \int_s \mathbf{J} \cdot d\mathbf{s} $$  We use the  to rewrite the left hand side; where \$c\$ is in the same direction with the magnetic flux \$\Phi\$.  $$ \oint_c \mathbf{B} \cdot d \mathbf{\ell} = \mu N I $$  (The integral on the left hand side results \$NI\$, because there are \$N\$ different wires on the winding.)  The magnetic field density inside these kind of cores are considered to be uniform. So, we can write  $$ B \ell_c \overset\sim= \mu NI \implies B = \dfrac{\mu NI}{\ell_c}; $$  where \$\ell_c\$ is the mean path lenght of the core.  We can find magnetic flux from the magnetic flux density we have found by using the cross sectional area of the core \$A_c\$.  $$ \Phi = BA_c = \dfrac{\mu NIA_c}{\ell_c} $$  By definition, inductance is the amount of magnetic flux generated per applied current, that is  $$ L \overset\triangle= \dfrac{\Phi}{I}. $$  So, we find inductance of the system as  $$ \boxed{ L = \dfrac{\Phi}{I} = \dfrac{\dfrac{\mu NIA_c}{\ell_c}}{I} = \dfrac{\mu NA_c}{\ell_c} }. $$  But, all other sources () give inductance of an inductor like this as  $$ L = \dfrac{\mu N^2A_c}{\ell_c}. $$  What is the mistake I did in my derivation? Please explain in detail. Defining commands/abbreviations that contain numbers I tend to use \newcommand to define macros for symbols I use often, e.g. \newcommand{\hankel}{H^{(1)}_0}.  One inconvenience of this approach is the fact that command names cannot include numbers.  What I ideally want is to map something like \H0 to H^{(1)}_0.  I imagine this could be done with some macro expansion/snippet package, or one might use \newcommand to define a command that takes a parameter, etc.  Before I start experimenting, though -- is there a canonical way of dealing with this problem? In a letter-class document that had no previous errors I am suddenly getting the error message:  "There's no line here to end" \opening{text}   I've used this file many times and today it starts giving this error. How do I troubleshoot this? Suppose $f(x)$ is an irreducible polynomial over $\mathbb Z$ of degree $n$. Is it always the case that there exist distinct $x_1,\ldots,x_{2n+1}\in \mathbb Z$ such that $f(x_1),\ldots,f(x_{2n+1})$ are all prime?  So far I've tested a few irreducible polynomials using mathematica, and this has held. The motivation is to use this as a test for irreducibility, as if $f(x)$ is not irreducible then it takes on at most $2n$ prime values, as either factor takes on $1$ or $-1$ at most $2n$ times. (I'd also be interested in learning if this bound can be improved).  This could potentially be expended to other rings of integers, i.e. $\mathbb Z[i]$, but in that case the minimal number of primes needed to certify that $f(x)$ is irreducible would increase as more units appear. What is the function of "do" in this sentence? Rarely, though, do countries introduce a single reform alone.   What function does do have in this sentence? How to find the most famous questions on Stack Overflow? How to find questions with   most comments most votes most viewed   I have seen following question, but seems like there is no easy way.   Is there way to bookmark a page so that the same URL can be used to update data (which will be very seldom) at each hit? Why Wi-Fi is getting turned-on automatically in iOS 11 Mysterious! Beamer itemize has no bullets after adding a few packages this is my first time using beamer.  I copied a template from the sharelatex page on Beamer  Which works, and \begin{itemize} shows bullets     But after adding a few more packages that I need, all the bullets are gone!    What is going on and how can I fix this?  \documentclass{beamer}  \usepackage[utf8]{inputenc}    \usepackage{amsmath}  \usepackage{amsthm}     %Theorem Environment  \usepackage{amssymb}  \usepackage{multirow}  \usepackage{cancel}  \usepackage{amsfonts}  \usepackage{graphicx}  \usepackage{subfigure}  \usepackage{upgreek}     \usepackage{mathtools}  \usepackage{thmtools}  \usepackage{enumitem}       %Information to be included in the title page: \title{Sample title} \author{Anonymous} \institute{ShareLaTeX} \date{2014}  \begin{document}    \frame{\titlepage}    \begin{frame}  \frametitle{Sample frame title}  \begin{itemize} \item  This is a text in first frame.  \item This is a text in first frame. \item This is a text in first frame.  \end{itemize}  \end{frame}  \end{document} Pressing Enter should not refresh the page False proof that $ρe^{iθ} = ρ$ and so complex numbers do not exist? My professor showed the following false proof, which showed that complex numbers do not exist. We were told to find the point where an incorrect step was taken, but I could not find it. Here is the proof: (Complex numbers are of the form $\rho e^{i\theta}$, so the proof begins there) $$\large\rho e^{i\theta} = \rho e^{\frac{2 \pi i \theta}{2\pi}} = \rho (e^{2\pi i})^{\frac{\theta}{2\pi}} = \rho (1)^{\frac{\theta}{2\pi}} = \rho$$ $$Note: e^{i\pi} = -1, e^{2\pi i} = (-1)^2 = 1$$ Since we started with the general form of a complex number and simplified it to a real number (namely, $\rho$), the proof can claim that only real numbers exist and complex numbers do not. My suspicion is that the error occurs in step $4$ to $5$ , but I am not sure if that really is the case. Keyboard layout indicator sometimes disappears Ubuntu 18.04.1 after some update I have two tables A &amp; B. Table A id | name | num  Table B id | date | roll  id in table B is a foreign key which relates to the id in table A. I want to get the contents of table B where id is given and also along with that data, I need the name whose id is given from table A. NOTE: cannot use multiple queries separated by commas; need to do both the SELECTs in one query. Shadows along edges of mesh in 3D View Add high-resolution-graphics and / or .svg-icons Referee says the proof is wrong, but it is not, what to do? About 3 months ago, my co-author and I submitted a mathematical paper to a journal. Yesterday, we got the editor's response and the paper has been rejected. The reason is that the referee thinks that our results are wrong or trivial.  However, we carefully read the referee's report and we conclude that the "errors" pointed out by the referee are not errors at all and that our proofs are correct. In all modesty, we think that the referee understood very poorly even the statements of our theorems.  Personally, this is the first time that such a situation occurs to me. I already have four papers published in such journal and the reports I got from the referees have been always really accurate.  What do you think is the best thing to do? Forget about and try another journal? Write an e-mail to the editor explaining why we disagree with the decision? Other ideas?  EDIT: Thank you very much for all your answers. At the end, we submitted our paper to another journal with only some slight edits we have already planned to do independently by the referee's report. Fatal error occurred, no output PDF file produced in php file We are using following code in .php script for generate .pdf file.  $result1 = exec("R CMD Sweave /var/www/html/r/r_latex_sweave.Rnw");  $result2 = exec("pdflatex /var/www/html/r/r_latex_sweave.tex");   but, we are getting this errors when we are executing .Rnw and .tex files.  ! I can't write on file `r_latex_sweave.log'. Please type another transcript file name:  ! Emergency stop !  ==> Fatal error occurred, no output PDF file produced!  Note: We have .tex and .Rnw folder in /var/www/html folder? What's going on here? I've installed the  on Ubuntu 17.10. Everything was cool, and as I was trying to hone and tweak the look of my desktop, at some point the shortcuts bar (dock?) on the left is duplicated.  (Click image to enlarge) The default, which normally disappears with Dash to Dock, is there underneath the one that usually shows up when I install Dash to Dock. Why? I've tried to go through the options for Dash to Dock, the GNOME Tweak Tool, and the regular Ubuntu settings, but I can't figure it out. Is there any way to kill a Thread? Inverse of function is continuous or not?