Do quantum physics apply universally at all scales?  Where do quantum physics apply?   Does the nucleus of an atom abide by the laws of quantum physics?   Like do we know the definitive/velocity position of a proton or that of a neutron-proton pair?   In other words, to which bodies does the Uncertainty Principle apply?   Are there wave functions for neutrinos, protons, neutrons, quarks or just for electrons?   And can you make a wave function for a larger body such as a molecule?   Where is the limit?
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 do I downgrade Minecraft to play on a server running an older version? Intuitive idea of the Lipschitz function I'm trying to understand intuitively the notion of Lipschitz function.   I can't understand why bounded function doesn't imply Lipschitz function.   I need a counterexample or an intuitive idea to clarify my notion of Lipschitz function.  I need help  Thanks a lot How do you use GRASS's v.kernel? I am flummoxed on how to use GRASS's v.kernel.  I have a vector layer of around 2.5 million points. I want to make a heat map using v.kernel to show concentrations, since I have variable instances with overlapping points, sometimes huge overlaps.  I've already gotten this vector layer in GRASS, and it displays just fine.  I've tried using GRASS's v.kernel command based on what I've seen here and on other forums, and I can't get it to do anything besides output a raster that's just a pink square.  Here's the command I'm using:  v.kernel --verbose input=master_grass7 output=master_grass7a_heatmap stddeviation=.0001   I've varied the stddeviation to all sorts of values from 1000000 to .000001, and it had no effect.  I've read the  repeatedly and don't really understand what it's getting at. At least, the instructions are on esoteric concepts, nothing practical. I've also checked the , and I'm not really understanding it, either. Yes, I can read C. The problem is it depends on a lot of stuff defined elsewhere in GRASS GIS.  I've also done a lot of Google searching, and I can't find a comprehensive guide. All that I'm getting are scattered copies of the v.kernel doc/man page or people who apparently got it to work without a fuss.  I've also checked up on the concept of kernel density estimation (KDE), and even then I don't see how to use the v.kernel command. That command appears to be a specific interpretation of KDE; its switches don't appear to correspond well to generic KDE concepts.  So back to the main question here: how can someone who is not intimate with GRASS product development use the v.kernel command? Is there a plain language translation available? Command for taking a screenshot to a new file Name finding problem with comment notification feature I just received the following in my Response pane (from ), but you can see it was meant for another user.  The @Robert line seems to have found 'Robert' in my name first, instead of Robert C. Cartaino.  I think the comment notification feature should match based on the closest match from the first character in a name (in posting order), and not just the first match found in posting order. I'm using wordpress multiste 3.3.1 I'm not gonna update it in the future. So I disabled all upgrade functions.  I want to remove the wordpress admin bar from both frontend as well as dashboard.  I can remove it from frontend using this code.  add_action( 'init', 'disable_admin_bar', 1 ); function disable_admin_bar() {     add_filter( 'show_admin_bar', '__return_false' ); }   But i couldn't find any solution to remove it from dashboard.   I don't want to use css solution to hide admin bar and I'm ready to edit the core files to remove it  Can anyone help me to remove it completely?. Thanks Test Class for a Custom Controller postfix doesn't work after iptables set up I have a small Problem that occurs from time to time.   Sometimes, when I copy things or when I put an object from the symbol library on my page, the whole file gets messed up. The screenshot shows it. I make the graphic on the right, Illustrator the ones on the left.   I have pixel snapping checked. Is there a way to tell Illustrator to align everything to pixels no matter what? This was the question of a test. My question is if my attempt to solve it is correct, and if it is, why is it correct.  $$\lim_{(x,y) \to (0,0), x+y \neq 0}{\frac{\ln(1-x-y)}{x+y} } $$  My attempt:   Let $\xi = -x-y $. Then $\xi \to 0$ whenever $(x,y) \to (0,0)$ and $x+y \neq 0 \iff \xi \neq 0$. (Is it then correct to say that the previous limit exists and is equal to the following iff the following exists? And why?):  $$\lim_{\xi \to 0, \xi \neq 0}{\frac{\ln(1+\xi )}{-\xi}}$$   If it is correct, then the limit exists and is $-1$. If it is correct, why is it correct? I entered the USA on a three month visa waiver program from Australia. I am about to return to  Australia and would like to come back again to the USA. How long do I have to wait until I can re-enter the USA for another 3 months? std::auto_ptr to std::unique_ptr What's a word for someone who is constantly asking for same thing? Objective-C - When to use 'self' I recently upgraded to 12.04 from 11.10 and since upgrading have been unable to log in to my user profile. The upgrade went okay and I can login to a guest session fine but whenever I try to login to my profile, after entering my password, I just return to the login screen.  I've changed my password in Root (passwd &lt;username&gt;) and can log in to tty1 with no issues, it's just in GUI I'm having problems.  I'm using a HP dv7 laptop, 32-bit Ubuntu install, Intel® Core™2 Duo CPU P7350 @ 2.00GHz × 2, Nvidia graphics.  Any help would be appreciated. Help + Noun + Gerund or Infinitive How to quickly send commands to nested tmux sessions? I have the following in my .tmux.conf  set -g prefix M-j bind-key j  send-prefix   I need to press (Atl+J) + (J) + bound-key to send something to the nested tmux session. I feel it is rather slow. Is there any better way? For example, I would love to be able to do (Alt+J) + (2x bound-key) to do stuff in the nested session. I constantly execute commands in the top tmux session instead of executing them in the nested one. Also, how come everybody binds prefix to C-a? I find it awfully slow and unpleasant to type this combination. Am I missing something? I'm a US passport holder. What documents do I need when I fly from the U.S. to Germany?  Assume I'm going for a few weeks of vacation.  Obviously I need my passport.  What about a "visa"?  Anything else? Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$ Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$. $AD,CF, BE$ are altitudes. Is there a simple way? I frequently prefer to look for questions on superuser .    I have never been able to determine how these search results are ordered.  Typically, search results are returned in order of relevance and the search help says they are "weighted heavily towards question title matches", but in this case, you would think that the search would order them based on whatever tab is currently selected (newest, hot, active)?  I ordinarily never stray outside of 'newest', but it's clear the results are not sorted by age.