This was discussed before proving the node theorem.
It is stated that if $\psi(x_0)=\psi'(x_0)=0$ at some $x_0$, then $\psi(x)=0,\forall x$.  Hence, we cannot have the wavefunction and its derivative vanishing at the same point.  My question is, how to prove the above statement?
Is there a way of setting culture for a whole application? All current threads and new threads? Is there a way of setting culture for a whole application? All current threads and new threads?  We have the name of the culture stored in a database, and when our application starts, we do   CultureInfo ci = new CultureInfo(theCultureString); Thread.CurrentThread.CurrentCulture = ci; Thread.CurrentThread.CurrentUICulture = ci;   But, of course, this gets "lost" when we want to do something in a new thread. Is there a way of setting that CurrentCulture and CurrentUICulture for the whole application? So that new threads also gets that culture? Or is it some event fired whenever a new thread is created that I can hook up to? I need a 'good' way to initialize the pseudo-random number generator in C++. I've found  that states:     In order to generate random-like   numbers, srand is usually initialized   to some distinctive value, like those   related with the execution time. For   example, the value returned by the   function time (declared in header   ctime) is different each second, which   is distinctive enough for most   randoming needs.   Unixtime isn't distinctive enough for my application. What's a better way to initialize this? Bonus points if it's portable, but the code will primarily be running on Linux hosts.  I was thinking of doing some pid/unixtime math to get an int, or possibly reading data from /dev/urandom.  Thanks!  EDIT  Yes, I am actually starting my application multiple times a second and I've run into collisions. postfix doesn't work after iptables set up I'm going through MSIL and noticing there are a lot of  instructions in the MSIL.  The MSDN article says they take no action and are used to fill space if the opcode is patched. They're used a lot more in debug builds than release builds.  I know that these kinds of statements are used in assembly languages to align later instructions, but why are MSIL nops needed in MSIL?  (Editor's note: the accepted answer is about machine-code NOPs, not MSIL/CIL NOPs which the question originally asked about.) Was Philip K. Dick able to watch a complete version of Blade Runner before his death or just unedited material?  The Blade Runner release date according to  and IMDb was 25 June, 1982. Philip K. Dick died a few months before, on March 2, 1982. Why do different humans look different? Although farmers appear to be able to tell their cows apart, cows look very much alike to me. And this similarity in appearance seems to be a general trait across the animal kingdom: one individual of one animal species looks much like another.  Why do human facial and body shapes vary so much?  I understand that human beings live in many different environments (e.g. hot and cold) and have adapted to these (e.g. through lighter or darker skin color), but there seems to be much variation that has no apparent evolutionary purpose. So does the difference have a purpose in itself? That is, did we evlove to vary in appearance, and what is the purpose of this variation? How do I transfer a file from a guest account on a MacBook Air? I recently received this rather amusing message while reviewing a user's first post:  Congratulations! This was only a test, designed to make sure you were paying attention. This post has already been removed, but thanks for taking time to leave feedback for the author.   What is the purpose of this test? How does the audit work? What happens if I fail? Why was the system expecting me to negatively review a good post, or positively review a bad post? A review is obviously an audit. Should I report it? Do review audits count toward the Reviewer badge? Do robo-reviewers dream of electric sheep? Having trouble adding objects to NSMutableArray in Objective C The Many Memes of Meta Catchphrases and concepts that spread from person to person are known as [memes], which, courtesy the Internet, can now explode across the Earth like a highly contagious virus (hence &quot;going viral&quot;). As with their real-life counterparts, some infectious diseases are global (pandemic), while others are endemic to specific regions. Stack Overflow, and now even more predominantly Meta Stack Exchange, have seen more than their fair share of these pathological social constructs spread through the user base. They are now ingrained units of our collective culture as SOpedians (a term which I hate, by the way). Just as travelers' immune systems can be assaulted by new diseases in new places, new users are increasingly likely to be miffed by an ingrained meme and left sitting scratching their heads. I therefore propose that this space be used to document the memes endemic to Stack Exchange's culture. Each meme should be listed in a separate answer and I hope that we as a community will be able to provide greater context to each one. Please actually explain each meme in a way understandable to those not already in the know. Especially considering that a lot of these memes aren't really understandable to newer users who weren't around in the early years of the network, or are based on system features that no longer exist.  On other Stack Exchange sites          [memes]: Upgrade OpenSSH 7.4 to later on RHEL I have a Red Hat Enterprise Linux server (7.5 x86_64). I have OpenSSH version 7.4. I was asked to upgrade it to a later version for security reasons: Nessus states that . However the Red Hat software and downloads does not have the latest package RPM.  I found some clues on where to get the latest package for OpenSSH. I found , however, I do not know on how to upgrade it and trust this website. I do not want the SSH and other configuration to be modified by the ugrade.  I did find links but however they are not useful, for example .  I would like to know how to upgrade OpenSSH without using yum. Only squares instead of letters and numbers are displayed in my calculator and other apps in Ubuntu 18.04 I don't know what I did wrong in my Ubuntu 18.04 OS. For some reason some of my apps look like this:    This also happens to other gnome apps like pdf-reviewer and Logs. Window title, menu bar etc. are all blank, display only squares.  *Problem solved: I downloaded Google Fonts, saved them in a new folder, they can be applied system-wide, but after I did some font settings using Google Fonts it didn't work. I changed the font of Interface with Tweaks-Tool, that was what causing the problem. I've always enjoyed solving problems in the complex numbers during my undergrad. However, I've always wondered where are they used and for what? In my domain (computer science) I've rarely seen it be used/applied and hence am curious.  So what practical applications of complex numbers exist and what are the ways in which complex  transformation helps address the problem that wasn't immediately addressable?  Way back in undergrad when I asked my professor this he mentioned that "the folks in mechanical and aerospace engineering use it a lot" but for what? (Don't other domains use it too?). I'm well aware of its use in Fourier analysis but that's the farthest I got to a 'real world application'. I'm sure that's not it.  PS: I'm not looking for the ability to make one problem easier to solve, but a bigger picture where the result of the complex analysis is used for something meaningful in the real world. A naive analogy is deciding the height of tower based on trigonometry. That's going from paper to the real world. Similarly, what is it that is analyzed in the complex world and the result is used in the real world without imaginaries clouding the problem?  The question:  is nice but covers a more mathematical perspective on interim results that make solving a problem easier. It covers different ground IMHO. Show that if the Riesz map is surjective on $H$, then $H$ is a Hilbert space Let $H$ be a vector space equipped with an inner product $(\cdot, \cdot)$ and $f:H\to H',\ f(x)=(\cdot,x)$ surjective. Now, why $H$  is a Hilbert space? The other direction is clear by Riesz' representation theorem but what about this? Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$. Let $f$ be an entire function that satisfies $|f(z)| \leq 1 + |z|$ for all $z\in \mathbb{C}$. Show that $f(z) = az +b$ for fixed complex numbers $a,b$.    The hint tells us to try and use Cauchy's Integral Formula on an arbitrary circle.    This is my attempt: Consider an arbitrary large circle with centre $0$ and let $\Upsilon$ be the contour around this circle.    Then $$\int_{\Upsilon} \frac{f(z)}{z^{n+1}} \mathrm{d}z = \frac{2\pi i}{n!}f^{(n)}(0).$$    Note that $$\int_{\Upsilon}\frac{f(z)}{z^{n+1}} \leq \int_{\Upsilon}\left|\frac{f(z)}{z^{n+1}} \right|\leq \int_{\Upsilon} \frac{1}{|z^{n+1}|} + \frac{1}{|z|^n}$$ and the right hand side is $0$ by Cauchy's Integral Formula. I'm not sure if the first equality is valid, and not sure where to go from here. I am trying to write the Euclidean algorithm in the following way:  $A = \lfloor A \div B \rfloor \times B + (\text{remainder of}) \: A \div B $   Now is there any symbol I can use  to say "remainder of A $\div$ B"? I know that in the C programming language there is the operator % for modulus; is that a valid symbol in maths? Can I write A % B? Or is there some other way? When customers buy things from a store, you say:  (1) Customers give ABC Store business.  If I "turn this around", can I say:  (2) ABC Store obtains or acquires business from its customers.  Do these verbs work in (2)? What is the solution to the Squirrel sequence of letters question? I can only move the origin point of the mesh that I selected in object mode, but not the whole mesh Did I set anything up by accident? Account not acting as an administrator correctly My account, david, is in the Administrators group on a Windows 7 machine.  I am still having problems with programs that I should be able to use, such as SQL Server. Specifically, my account seems to not have correct permissions when I am working.  I know with an Administrator account I should have full access. How can I force my account (david) to act like an admin account and have full access to everything?