So this question is a direct follow on from  I am trying to get an expression for $\frac{d\left&lt;p\right&gt;}{dt}$. I have my working out below, which was thanks to the 's help, (not to mention all the patient people in the mathematics chatroom) I have got to this expression: $$ i\hbar \left( \int\limits_{-\infty}^{+\infty}{ \frac{-i\hbar}{2m} \dfrac{\partial^2 \Psi^*}{\partial x^2} \frac{\partial \Psi}{\partial x} + \frac{i}{\hbar}V \Psi^* \frac{\partial \Psi}{\partial x} }dx + \int\limits_{-\infty}^{+\infty}{ \Psi^* \frac{\partial}{\partial t} \frac{\partial \Psi}{\partial x} }dx \right). $$ And now I'm stuck. What can I do about $$ \int\limits_{-\infty}^{+\infty}{ \Psi^* \frac{\partial}{\partial t} \frac{\partial \Psi}{\partial x} }dx $$ In particular how to deal with $$ \frac{\partial}{\partial t} \frac{\partial \Psi}{\partial x}? $$ With the $\partial t$ in play I don't know how solve the integral... As before, I really would appreciate hints to get me moving in the right direction more than an outright solution. My working so far We are given $\left&lt;p\right&gt;$ in the text, which is determined by computing $\frac{d\left&lt;x\right&gt;}{dt}$ and multiplying by $m$. Lets just start with what we know: $$ \left&lt;p\right&gt; = \int{\Psi^*\left[-i\hbar \frac{\partial}{\partial x}\right]\Psi}dx. $$ So taking the time derivative, $$ \frac{d\left&lt;p\right&gt;}{dt} = \frac{d}{dt}\int{\Psi^*\left[-i\hbar \frac{\partial}{\partial x}\right]\Psi}dx. $$ We probably should at this point pause, and listen to Ted, (). So take out the constants before going any further. We get, $$ -i\hbar \frac{d}{dt}\int\limits_{-\infty}^{+\infty}{         \left(             \Psi^*                 \left[                     \frac{\partial}{\partial x}                 \right]             \Psi         \right)         }dx. $$    Bringing the time derivative into the integral, gives us $$ -i\hbar \int\limits_{-\infty}^{+\infty}{\frac{\partial}{\partial t}\Psi^*\left[\frac{\partial}{\partial x}\right]\Psi}dx. $$ Then differentiating with the product rule yields, $$ -i\hbar \int\limits_{-\infty}^{+\infty}{ \frac{\partial \Psi^*}{\partial t} \frac{\partial \Psi}{\partial x}+  \Psi^* \frac{\partial}{\partial t} \frac{\partial \Psi}{\partial x} }dx. $$ Now we have two terms in our integral, let's split em up. Let's consider the left handside first, we have $$ \int\limits_{-\infty}^{+\infty}{ \frac{\partial \Psi^*}{\partial t} \frac{\partial \Psi}{\partial x} }dx. $$ By Schrödinger this can become, $$ \int\limits_{-\infty}^{+\infty}{ \left(\frac{-i\hbar}{2m} \dfrac{\partial^2 \Psi^*}{\partial x^2} + \frac{i}{\hbar}V \Psi^* \right) \frac{\partial \Psi}{\partial x} }dx. $$ Expand to get, $$ \int\limits_{-\infty}^{+\infty}{ \frac{-i\hbar}{2m} \dfrac{\partial^2 \Psi^*}{\partial x^2} \frac{\partial \Psi}{\partial x}+ \frac{i}{\hbar}V \Psi^* \frac{\partial \Psi}{\partial x} }dx. $$ So, just to review, our full problem can be written as, $$ i\hbar \left( \int\limits_{-\infty}^{+\infty}{ \frac{-i\hbar}{2m} \dfrac{\partial^2 \Psi^*}{\partial x^2} \frac{\partial \Psi}{\partial x} + \frac{i}{\hbar}V \Psi^* \frac{\partial \Psi}{\partial x} }dx + \int\limits_{-\infty}^{+\infty}{ \Psi^* \frac{\partial}{\partial t} \frac{\partial \Psi}{\partial x} }dx \right). $$
I am currently working through the problems in , with the goal of hopefully understanding how magnets work. At the moment I am a little stuck on one of the early problems in the first chapter. And I would like a Hint about how to proceed. The problem is to solve the time derivative of the expectation value of momentum of a particle. ie: $$ \frac{d\left&lt;p\right&gt;}{dt}. $$ My working so far Just prior to that question the text gives an expression for momentum, $$\int\limits_{-\infty}^{+\infty}{\Psi^*\left[-i\hbar \frac{\partial}{\partial x}\right]\Psi}dx, $$ (Where $\Psi$ is a function satisfying Schrödinger's equation, $i$ is the square root of negative 1, and $\hbar$ is Planck's constant divided by $2\pi$.) So my initial approach was to try and differentiate this with respect to $t$. $$ \frac{d}{dt}\int\limits_{-\infty}^{+\infty}{\Psi^*\left[-i\hbar \frac{\partial}{\partial x}\right]\Psi}dx. $$ However I didn't know how to do that, so I asked around in the maths chatroom, and got a lot of help. Specifically  from @RobJohn: $$ \begin{align} \int vv'\,\mathrm{d}x &amp;=vv-\int vv'\,\mathrm{d}x\\ &amp;=\frac12vv+C \end{align} $$ So I suppose it would follow that, $$ \begin{align} \int\limits_{-\infty}^{+\infty}{         \left(             \Psi^*                 \left[                     \frac{\partial}{\partial x}                 \right]             \Psi         \right)         }\,\mathrm{d}x &amp;=  \left[\Psi^* \cdot \Psi\right]_{-\infty}^{+\infty} - \int\limits_{-\infty}^{+\infty} {\Psi\frac{\partial \Psi^*}{\partial x} }\,\mathrm{d}x\\ &amp;= \frac{1}{2}|\Psi|^2 \Big|_{-\infty}^{+\infty}, \end{align} $$ And then, $$ \begin{align} &amp;\frac{d}{dt}\int\limits_{-\infty}^{+\infty}{\Psi^*\left[-i\hbar \frac{\partial}{\partial x}\right]\Psi}dx \\&amp;=-i\hbar \frac{d}{dt}\left( \frac{1}{2}|\Psi|^2 \Big|_{-\infty}^{+\infty} \right). \end{align} $$ But this feels wrong. I'm not sure exactly why. (Maybe it's just because it is the limits of my maths)  For reference, regarding what I understand, my maths is pretty low-level, I took a course in undergrad calculus over 10 years ago and only just passed that at the time, and my physics knowledge is not much further than that of an enthusiastic lay person.
Hide back faces in 3D View? How do you hide back faces so that you only see faces when its normal is facing the camera? When exporting it for use in a game, the face is rendered in only the direction of its normal, so this would be useful to have something similar. Need to understand parallel query execution error Today we experienced a degradation in performance on our production sql server.  Durring the time this occurred we logged several "The query processor could not start the necessary thread resources for parallel query execution" errors.  The reading that I've done suggests that this has to do with how many CPUs to use when executing a complex query.  However when I checked during the outage our CPU Utilization was only at 7%.  Is there something else this could be referring too that I haven't come across yet?  Is this a likely culprit of the performance degradation or am I chasing a red herring?  My sp_configure values for this are as follows:  name                                minimum maximum config_value run_value cost threshold for parallelism      0       32767   5            5 The iOS-app should provide (at least) the same features as the site and the ability to edit your profile is not so unimportant.  In my opinion, the user should be able to change the every single info-field in his profile (including, but not limited to nickname, description, profile picture) by pressing an "Edit" button which should be located somewhere on his or her profile view. Z-axis issue with the floating review info panel, permits various elements to flow over it I was having a look at an old question of mine when I browsed the  from the timeline. I scrolled downwards and realized the Review completed panel comes along for the ride. While that might be , tags flowing over top of it as pictured below probably isn't.  Here's a .gif of the Question and Duplicate tabs flowing over it as well. Note that the timeline button also flows over. If vote buttons are present, they will also flow over it.  Reproduced on Chrome and Microsoft Edge. Update Per  by Tiago Martins Peres, this issue also happens in other Review types, namely Late Answers, First Posts and Low Quality Posts. In addition to that, it is causing the action buttons on reviews to become unclickable if you scroll low enough.  As a temporary workaround, you can use 's , which  this issue. 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. Forge CBC-MAC by creating a new message, given the MAC of two messages In my cover letter I want to write that I am a graduate student in statistics. But I am not sure about the "in". So what is correct?     I am a graduate student in statistics.      I am a graduate student of statistics. I'm reading through  for the , which contains this figure on page 16:    This is of course an instrumentation amplifier that apparently uses an inverting amplifier's output instead of a ground in the lower-right corner of the above figure, but what really perplexes me is the 100 k&Omega; resistors attached directly to the noninverting inputs of three of the four amps. I don't recall seeing an instrumentation amplifier circuit in books or application notes that have them, and all of the instrumentation amplifiers I've built using the three op-amp scheme works fine without them.  The datasheets specifies an input resistance of 1012 &Omega;, which is 10,000,000 times greater than 100 k&Omega;, so it doesn't seem to add anything to the already high-impedance JFET inputs. I thought perhaps it has something to do with input bias currents, but that's just me making a wild stab in the dark.  Curiously, figure 26 in the same datasheet (page 18) shows a two-op-amp version of an instrumentation amplifier without the 100 k&Omega; resistors at the noninverting op-amp inputs!  What's the purpose of the 100 k&Omega; resistors at the noninverting inputs in the above circuit? Am I missing something completely obvious? Operator font in beamer/metropolis When using the metropolis theme for beamer, I get text and math in Fira Sans, except for math operators. I compile the following MWE using LuaTeX.  \documentclass{beamer}  \usetheme{metropolis}  \begin{document}    \begin{frame}     Ordinary text.     \[ a^2 + b^2 = \sin^2(x) - \mathsf{y} + \mathrm{z}  \]   \end{frame}  \end{document}   The outcome for me is that a, b, 2 and x are set in Fira Sans Light Italic, and y is set in Fira Sans Light, but sin is set in the sans font of (I guess) Latin Modern. (The z is also in Latin Modern, but this is expected behaviour from beamer.)  Unsurprisingly, I get the same result if I replace \usetheme{metropolis} with  \usepackage[no-math]{fontspec} \setsansfont[ItalicFont={Fira Sans Light Italic},   BoldFont={Fira Sans},   BoldItalicFont={Fira Sans Italic}]%   {Fira Sans Light}   I guess that this is to do with beamer's patching parts of the math fonts to match the text font (see ). However, I don't understand the font system well enough to modify this.  There was , but I've no idea how to apply that answer when using fontspec, or if this is even possible.  Is there a way to change the operator font to match the upright/sans math font (i.e., Fira Sans Light)? As you can see on this screenshot of 's Guake he has a startup message of ASCII art when he opens it, and that's what I'd like to do, can someone help me? How to contact professors for PhD vacancies? I know many master's students who get an opportunity to talk to their potential PhD advisors well before applying. In most cases this opportunity is available by the professors with whom they worked for their master's. Moreover, there are many others who establish a contact with professors by mailing them and enquiring about PhD vacancies.   My questions are:   How important is knowing an advisor prior to applying for PhD?  Does an email interaction play a vital role when the department makes its admit decisions? If email contact is important, can a student send out mails to 2-3 professors (working in the same area) in case one of them does not bother to reply? To sum up, is applying of any use (especially in top universities) when you have no contacts and only your credentials to bank on? What Constitutes Spam? Over the course of the past several months, there have been one or more users who have been spamming about an XML parsing alternative named &quot;VTD-XML&quot;. I have occasionally assisted the moderators by pointing these answers out to them, and they have responded by deleting the answers, and the offending user (which hasn't stopped this person from immediately creating another user account and continuing). Now, there is a user , who claims to be the actual author of VTD-XML. In my mind, several of his answers, like his  to  looks a great deal like the original spam.  has asked me why I consider his answer to be spam. I decided to do so in public, in an attempt to get him to engage with this community, assuming he's not another sock puppet of the original spammer.  My reason is simple: he's been answering with one or two lines of text, followed by the exact same link to the exact same site that the spammer was using:  VTD-XML may well be worth a look as it is 1/3~1/5 the memory usage of DOM   Now, maybe I'm wrong. Maybe this does not constitute spam. Maybe Mr. Zhang can explain to us why we should not treat these posts as spam. Let's see.  Somehow, I missed the fact that in the same question, on July 31 2009:  how about vtd-xml  http://vtd-xml.sf.net   This one was from a user named &quot;Jimmy Zhang&quot;, which has since been deleted. Should I not be suspicious? Additionally, as pointed out by , he's answering a question about Delphi by posting a link to a site that doesn't even mention Delphi! Throughout the nonsense with the sock puppets, I kept asking for some real engagement from the sock puppet. It all just made VTD-XML look bad that instead of truly answering questions, we just kept getting incessant spam against old XML questions. Appeal Mr. Zhang, if you're not just desperately spamming StackOverflow because your product isn't selling, then please answer appropriate questions in a way that will actually help someone use your product to solve their problems. ORA-00979 not a group by expression I'm looking for a good way to perform multi-row inserts into an Oracle 9 database.  The following works in MySQL but doesn't seem to be supported in Oracle.  INSERT INTO TMP_DIM_EXCH_RT  (EXCH_WH_KEY,   EXCH_NAT_KEY,   EXCH_DATE, EXCH_RATE,   FROM_CURCY_CD,   TO_CURCY_CD,   EXCH_EFF_DATE,   EXCH_EFF_END_DATE,   EXCH_LAST_UPDATED_DATE)  VALUES     (1, 1, '28-AUG-2008', 109.49, 'USD', 'JPY', '28-AUG-2008', '28-AUG-2008', '28-AUG-2008'),     (2, 1, '28-AUG-2008', .54, 'USD', 'GBP', '28-AUG-2008', '28-AUG-2008', '28-AUG-2008'),     (3, 1, '28-AUG-2008', 1.05, 'USD', 'CAD', '28-AUG-2008', '28-AUG-2008', '28-AUG-2008'),     (4, 1, '28-AUG-2008', .68, 'USD', 'EUR', '28-AUG-2008', '28-AUG-2008', '28-AUG-2008'),     (5, 1, '28-AUG-2008', 1.16, 'USD', 'AUD', '28-AUG-2008', '28-AUG-2008', '28-AUG-2008'),     (6, 1, '28-AUG-2008', 7.81, 'USD', 'HKD', '28-AUG-2008', '28-AUG-2008', '28-AUG-2008'); Apache error "Could not reliably determine the server's fully qualified domain name" Should one downvote answers to off-topic questions? It annoys me when people post answers to obviously off-topic questions like , especially after those questions have already received several close votes. Migrations seem to happen rather infrequently these days, so there's probably no reputation to gain for questions that are likely to be closed. And although sure, the answer may help the OP, it also encourages bad behavior (posting off-topic questions.)  Is it appropriate to downvote these answers?   Personally, I think I could make a case for both sides. Why particle hole symmetry and chiral symmetry are called symmetries? $PHP^{-1}=-H$ (particle-hole symmetry) and   $\Gamma H \Gamma^{-1}=-H$ (chiral symmetry)   I understand why we get the negative signs but im just a bit confused as to why such equalities mean $H$ is particle hole and chiral symmetric.   When we say $H$ is symmetric under some operation, like time reversal,  don't we usually mean that $H$ is invariant under the said transformation?  $THT^{-1}=H$ if $H$  is time reversal symmetric.  On the contrary, we say $H$ is symmetric under particle hole and chiral operations when $H$ picks up a negative sign. This seems to contradict our usual convention of what we mean by $H$ being symmetric(invariant). How to remove duplicate values from a multi-dimensional array in PHP Extension “RANDR” missing on xvfb My system:  $lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 14.04.3 LTS Release:        14.04 Codename:       trusty   Xvfb:  $ dpkg -s xvfb Package: xvfb Status: install ok installed Priority: optional Section: x11 Installed-Size: 2140 Maintainer: Ubuntu X-SWAT &lt;ubuntu-x@lists.ubuntu.com&gt; Architecture: amd64 Multi-Arch: foreign Source: xorg-server Version: 2:1.15.1-0ubuntu2.7 Provides: xserver   Current problem:  Xvfb do not support RANDR extension, even if I add the flag:  +extension RANDR   If I run xdpyinfo, RANDR is not on the list. It's a missing feature or a bug. I found a reference here with a patch:   And looks like that in other distros like debian, there is already a testing build of Xvfb with support:   I am trying to run a program throught Xvfb, and it returns the following error:  Xlib:  extension "RANDR" missing on display ":99".   The program works if I run it via ssh/command line. The problem appears to be the the lack of support for "RANDR" in xvfb.  My question is: what is the easiest way to get xvfb with "RANDR" support in my system? MySQL Results as comma separated list I need to run a query like:  SELECT p.id, p.name,         (SELECT name            FROM sites s           WHERE s.id = p.site_id) AS site_list   FROM publications p   But I'd like the sub-select to return a comma separated list, instead of a column of data.  Is this even possible, and if so, how?