Is there a hard upper bound to the deBroglie wavelength of a particle with vanishing momentum? This is probably a stupid and simple question, but does the heisenberg uncertainty principle set this upper bound? That knowledge of the momentum is limited, so it can't reach a very low value and thus have a very large (visible) debroglie wavelength? I am figuring if you wanted to test this on a macroscopic particle you would need it frozen to near-absolute zero, but I assume QM comes in and makes it impossible to see visible wavelengths with the naked eye. Thanks!
Validity of naively computing the de Broglie wavelength of a macroscopic object Many introductory quantum mechanics textbooks include simple exercises on computing the de Broglie wavelength of macroscopic objects, often contrasting the results with that of a proton, etc.  For instance, this example, taken from a textbook:     Calculate the de Broglie wavelength for      (a) a proton of kinetic energy 70 MeV      (b) a 100 g bullet moving at 900 m/s   The pedagogical motivation behind these questions is obvious: when the de Broglie wavelength is small compared to the size of an object, the wave behaviour of the object is undetectable.  But what is the validity of the actual approach of applying the formula naively? Of course, a 100g bullet is not a fundamental object of 100g but a lattice of some $10^{23}$ atoms bound by the electromagnetic force. But is the naive answer close to the actual one (i.e. within an order of magnitude or two)? How does one even calculate the de Broglie wavelength for a many body system accurately?
How to concatenate a variable number of csv, removing their header rows? What is the most bizarre thing you have seen done with TeX I think the questions says it all! :)  By TeX, I mean any derivative of TeX as long as the code is clearly a derivative of TeX, i.e. that it could belong on TeX.SX (and not pure Lua for example).  I'll give two answers myself so you see what I mean. Can't save my render as an image I seem to be having issues when I try and save the output file as a .png, or .jpeg for that matter. I've set up my user preferences, File, Render Output to my desktop as well as render output in the editor window. What am I missing here? I'm obviously very new to this program and your help would be appreciated. Thanks for your time I no longer use the service that I originally used to register, and would like to change the service I use to log in, or at least add a second account.  Is this possible? How do I change my login provider or associate a backup method to log in?     For more information, see "" in the . NSDate Format outputting wrong date Associativity of symmetric difference of sets By $A\oplus B$ we denote the symmectric difference of two sets. The definition is $A\oplus B =(A\setminus B) \cup (B\setminus A)$. Now I hope to show that $A\oplus (B\oplus C) = (A\oplus B)\oplus C$. I remember that there's an elegant proof, but I forget its detail. (The first step is to show $A\oplus (A\oplus B) = B$, and maybe applying this formula, we can obtain associativity.) Is there a way of installing Ubuntu (Windows Subsystem for Linux) on Win10 (v1709) without using the Store? The Microsoft Store app is disabled by Group Policy by my university. I have administrator rights on my computer and I was wondering if there was a way of installing Windows Subsystem for Linux (WSL) directly? Or maybe via Chocolatey or some other command line method? I would like to download and install the Ubuntu  on windows without using the Microsoft store.  Note that since version 1709 (Fall Creator's Upgrade), only enabling Developer Mode is no longer sufficient. How do I add myself into the sudoers group? Possible Duplicate:          I've added myself back into the admin's group I think, by following   But I still can't do commands like:  sudo aptitude update   I get the message  oshirowanen is not in the sudoers file.  This incident will be reported.   How do I add myself into the sudoers group now that I am in the admin group? I try to initialize an array in bash-4.2 next way:  ring=() ls -las | tail -n +4 | while read line &gt; do &gt; ring+=("$line") &gt; echo ${ring[-1]} &gt; done 3924 -rw-r--r-- 1 username group 4015716 Mar 23 15:14 script.jar 4 -rw-r--r-- 1 username group 9 Feb 29 12:40 rec.lst 5541 -rw-r--r-- 1 username group 5674226917 Mar 28 15:25 debug.out 8 -rw-r--r-- 1 username group 6135 Mar 25 12:16 script.class 8 -rw-r--r-- 1 username group 6377 Mar 25 11:57 script.java 8 -rwxr-xr-x 1 username group 4930 Mar 8 15:21 script-0.0.0.sh 8 -rwxr-xr-x 1 username group 6361 Mar 28 15:27 script-0.0.1.sh echo ${ring[0]}  echo "${ring[0]}"  echo "${ring[@]}"   What is wrong, why i get empty array after the finish of the loop? tcpdump : lost packets I extracted simple example:  require 'pp' x = 1..3 pp x.map do |i| {:value =&gt; i, :double =&gt; (i*2)} end pp x.map { |i| {:value =&gt; i, :double =&gt; (i*2)} }  pp(x.map do |i| {:value =&gt; i, :double =&gt; (i*2)} end) pp(x.map { |i| {:value =&gt; i, :double =&gt; (i*2)} })   I am wondering why first pp produces:  [1, 2, 3]   While all the oders are giving:  [{:value=&gt;1, :double=&gt;2}, {:value=&gt;2, :double=&gt;4}, {:value=&gt;3, :double=&gt;6}]   I assume it has something to do with operator precedence. Where can I find good explanation? How do I retrieve only the needed line from terminal output? Should a toggle button show its current state or the state to which it will change? How do you make corrections to a published paper? Can we omit a duplicated preposition? Is on needed a second time in this sentence?        There is a bad effect either on human health or environment.    There is a bad effect either on human health or on environment. Where are minecraft languages stored and how can I add a new one? Short-lived sci-fi series with a former astronaut turned superhero (or maybe a police officer?) using his spacesuit for his "powers" Plot Details/Summary I only watched an episode or two of this one, so I can't recall a whole lot about it.  The protagonist is a former astronaut of some sort, who makes it his mission to clean up the crime in his city.  He might have been a police officer in his &quot;new life&quot; or he might have decided to become a sort of quasi-superhero.  In either case, I distinctly recall his space suit being the gimmick that makes him an effective crime fighter in the show.  I seem to recall the protagonist being a young, dark-haired man, and I think he had a friendship or an alliance with a young woman (maybe a fellow cop, or someone from the space program?).  I don't think there were alien beings in the show.   The criminal threats were all quite terrestrial, IIRC. Timeframe and other Publication Details This was a syndicated tv show I saw on American television, probably around the late 90s to early 2000's.  I believe the show was filmed in Canada, though I'm not certain.  I don't think it lasted very long - it was pretty dreadful.  I can say for certain the show is not Space Cop or Gerry Anderson's Space Precinct. How to divide LaTeX table cells vertically? I want my table to have separated cells. Basically double lines but I can't figure how to have horizontal lines disconnected. I tried \hline and \cline but those connect too.  This is best I can do:    This is how I want my table to look:   \begin{tabular}{|c||c||c||c|}   \hline   \multicolumn{2}{|c||}{First Cell}&amp;   Second Cell&amp;   Third Cell\\   \hline   \hline   \begin{tabular}{@{}l@{}} Data\\ Data\\ Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}\\    \hline  \end{tabular} If someone could claim me as a dependent, but they will not, am I required to check the "Someone can claim me..." box on my 1040? Let's say that an adult is living with his parents.  He meets all of the  of his parents.  Now let's say that he wants to file a tax return and claim the , as he did not receive any of the stimulus payments in 2020.  His parents decide not to claim him as a dependent on their taxes.  Can he leave the &quot;Someone can claim me as a dependent&quot; box on his  unchecked and claim the Recovery Rebate Credit?  This does not apply to me, but it could apply to many people this year, with the new Recovery Rebate Credit putting people in the situation where it could be advantageous to not be claimed as a dependent. Surprisingly, the  do not provide any guidance on checking this box in any way, that I can find.  I have seen it asserted many times in answers and comments here on Money.SE that because the form says, &quot;Someone CAN claim...,&quot; the box must be checked whether or not anyone actually will claim them.  But I have not yet found this explicitly stated in any official IRS website or publication.  The ideal answer here will cite an official source. Moving a doorbell transformer Can a doorbell transformer that is on the outside of a wall be place inside the wall behind the drywall. I’m concerned about it getting too hot. Mine is in the kitchen by the ceiling lights