How do you arrive at the de-Broglie wavelength? Ok, so I understand that it was a hypothesis, but still I have a couple of questions that have boggled my mind for the past few months.  1) How did de-Broglie obtain his formula? Did he guess it on experimental basis?  2) I have seen two types of ad-hoc derivations.    Using mass-energy equivalence  The main idea of this derivation is that you have $E = mc^2$ and $E = h\nu$ and equate them both to get $\lambda = \dfrac{h}{mc}$, for a photon, and for a particle moving with a velocity $v$, you have $\lambda = \dfrac{h}{mv}$.   To me this approach seems plain wrong as it messes up conceptual stuff. From what I know, $E = mc^2$ is the energy for a particle at rest, and $E = h\nu$ is for the energy of a photon of frequency $\nu$. Yes, they are energies, but not energies of the same kind. How can you equate the two? It feels wrong.   This one is not quite messy as the last one, but -    You have $E = \sqrt{p^2c^2 + m^2c^4}$ and for a photon with zero rest mass, you have $E = pc$. Equating this with $E = h\nu$, you have $p = \dfrac{h}{\lambda}$ or $\lambda = \dfrac{h}{p}$. Now we extend the same logic to particles having mass they must also have a de-Broglie wavelength $\dfrac{h}{p}$. But we started with zero rest mass, then how does it apply to electrons and other particles having non-zero rest mass?  3) Am I stressing too much on derivations, and just not letting it be what it is? Since it was a hypothesis, and cannot be proven (like a theorem).  Anyways, could you elaborate on the mistakes that I have spoken about in 2)? Or is it that I am conceptually mistaken? And also answer 1) and 3)?
Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from? I'm curious where the  $p=\frac{h}{\lambda}$ comes from?   I know that for light (which has no rest mass), the following is true:  $E=pc$ and $E=hf$  so,  $$pc=hf \Rightarrow p=\frac{hf}{c}=\frac{h}{\lambda}$$  But how is the expression $p=\frac{h}{\lambda}$ obtained for a massive particle where $E\neq pc$? I've read some people claim that the expression can be derived, and others saying it's an experimentally verified relationship.
A gold reviewer badge? How to disable X server autostart in Debian Jessie? This problem is bugging me for some time.     $f:(X,\mathcal{T}) \to (Y,\mathcal{T}')$ is a continuous bijection where $(X,\mathcal{T})$ is compact and $(Y,\mathcal{T}')$ is $T_2$ (i.e. Hausdorff and $T_1$). Then show that $f$ must be a homeomorphism.   So far I have failed to understand any relation between the compactness of domain and $T_2$-ness of the range. I tried in vain to prove that $f(U)$ is open in $(Y,\mathcal{T}')$ whenever $U$ is so in $(X,\mathcal{T})$. I know $f$ makes $X$ and $Y$ respectively $T_2$ and compact and hence makes both of them $T_4$ spaces. But that is not coming to any use. I would be glad if someone helps me with a solution. Thank you. Say I had  and I used  on something, could I respond to Cloudshift bringing the creature back into play with  or something similar? Filtered Review Queue doesn't show any audits Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$? Filling a polygon with a pattern of insets How to create a circular shaped grid, similar to a manhole cover I’m trying to create a circular shaped grid, similar to the one in the pic. That’s my first attempt, created by arranging several cylinders with an Array modifier and then cutting the holes via the Boolean modifier.  Now you will probably notice that it looks not elegant in any way. I’d like to have the holes perfectly arranged and in a correct order, so that there are no half holes at the border of the mesh, for example.  How would you do this?   I tried working with Dupliverts but that didn’t work out well. Add asterisk after labels in enumerate I would like to add an asterisk after certain labels in the enumerate environment. So for example  \documentclass{article} \begin{document}  \begin{enumerate}     \item Kuttel     \item* Daddeldu \end{enumerate}  \end{document}   but without the space between 2. und *. How to show (or hide) a hidden file I wanted to add classpath to my JDK. While searching a way to do it I noticed everyone open .profile file using terminal. But when I want to open and edit it with a text editor I couldn't see that file in Home folder.  Can someone tell me why is this. And also if possible how can I access .profile in home folder the GUI way. How can I have `date` output the time from a different timezone? I have a server running with the timezone set to UTC. It seemed like that was generally a good practice (please correct me if I'm wrong).  Anyhow, one of the servers I connect to, in order to scp files, is running on EDT and stores files that I need to copy in the format /path/to/filename/data20120913  I looked at trying to rsync files using something like find's -mtime -1 flag for files modified in the last day, but I didn't have any luck.  I don't mind just using scp to copy the current day's file, but as of right now there is a 4-hour window where running date +%Y%m%d will give a different day on each server and that bugs me a little.  Looking through man date I see that I can have the time output as UTC, but I don't see a way to have it output as another timezone like EDT  I suppose I could also use something like the GNU date extension date -d 20100909 +%s to get the date in seconds from the epoch, apply a manual 4 * 60 * 60 second calculation, and see about rendering that as a date - but then when daylight time kicks in it will still be an hour off.  Is there a simpler way to output the date in a YYYYMMDD format for EDT on a server that is set to UTC ? There has been some discussion about getting notified on comments to questions or answers that don't belong to you, and the long-standing wish to be able to keep track of new answers or developments in questions asked by other people.  Previous discussion in regards to subscribing to questions:                  (very similar to this one)      In regards to subscribing to comments:                    The general feeling - at least here on meta - seems to be against broadening the notification rules, out of fears of useless notifications to flood users' inboxes, turning SO into more of a discussion forum than it should be, etc.   Here's a suggestion that would keep the user 100% in control what they get notified about, not generate any notifications by default, and require only minimal modifications to the User Interface.  Each question and each comment area would get an envelope symbol.    it is inactive (=white) by default.  When those envelopes are hovered over, the tooltip says click to subscribe or something.  When clicked on, the envelope lights up in green or some other colour (but different from the actual notification envelope's orange to avoid confusion.) You are then subscribed to any updates to that question or comment thread.    For each subscription, you receive notifications in the "responses" tab, as if you were the owner of the comment or question.     To unsubscribe from a question or comment thread, you open the page, and click the green envelope. It turns back white, and the notifications disappear from your responses tab (if technically possible - otherwise, there just won't be any new ones added.)    No further functionality, like managing subscriptions or anything, is necessary IMO. If the flood of notifications from a subscribed question starts to annoy you, you just open it and unclick the envelope. Done.   It would make it possible to leave a comment to a newbie's question and make sure their answer reaches you even if they don't know they need to address you using @username You could subscribe to those "oh, I'd like to know the answer to that" questions and receive active notification, instead of them getting forgotten in your favourites list You could subscribe to discussions you are interested in the outcome of, but don't want to participate in. It would (in my opinion) sort out a number of woes aired by many users in a good way, without adding annoyances to those who like the system just fine the way it is. It would not require a change in the visible layout. As far as I can see, the space the envelope would need to be is empty everywhere.   I don't know SO under the hood of course, but technically, the system would be doing what it's doing already, notify question owners of updates - just that the circle of internal "owners" would grow. executing web service using postman Is the product of symmetric positive semidefinite matrices positive definite? Let's say I use a  with a lot of code inside. To improve readability and reusability I'd like to use helper/private methods. However, a Drupal .module file is not a class.  The idea is to split big methods from this file into more readable and reusable smaller methods.  What is the correct way to call helper/private methods from a Drupal .module file? Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal. Prove: Let $R$ a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.     I got stuck on this. I understand that every ideal is generated by finitely many elements. Here is my approach:  It's enough to prove the following implication: $$ R/I \ \text{is a domain} \quad \Rightarrow \quad R/I \ \text{is a field}$$ Then only finding an inverse is left. So let $x \in R$ in arbitrary. We have to find an inverse element of $x+I \in R/I$, that as an element y so that $x \cdot y \in I+1$. We denote $I = (x_1, x_2, \cdots, x_n)$.  Now I have to find y so that $xy -1 = r_1 x_1+ r_2 x_2 + \cdots + r_n x_n$. This is where I no more knew what to do.   Your advise will be appreciated. Factoring Quadratics Is there a method to find which numbers to use when simplifying quadratics?   For example $x^2 + 5x + 6$ is easy enough to find, but what if I have bigger numbers, or I have this quadratic expression: $x^2 + 7x – 6$, then it gets very hard to think of a valid simplification.  EDIT: Here's an example: $(x^2 + 5x + 6)/(x + 2)$. When simplifying the first half we get $(x + 2)(x + 3)/(x + 2)$, then we can cancel out $(x + 2)$ and the answer would be $(x + 3)$. The question is: How to always find the right numbers which to put in? (in this example they where 2 and 3) Java: Avoid inserting duplicate in arraylist @class vs. #import How can I move my /home directory to another partition if it's already part of the / partition?