Functional Analysis for Quantum Mechnanics
A book on quantum mechanics supported by the high-level mathematics
Every irreducible polynomial $f$ over a perfect field $F$ is separable.   Can you check my proof? Assume that $f$ is irreducible but inseparable. So we have $f=\sum_i h_ix^i$ and $f^p=\sum_i h_i^px^{ip}$. Now I use Frobenius mapping $\phi (f)=f^p=(\sum_i h_ix^i)^p=\sum_i h_i^px^{ip}$ so it is reducible. Contradiction. Should I also show for char(F)=0? MacBook [Pro] - how many displays, what resolution/frequency? How can I get file extensions with JavaScript? See code:   var file1 = "50.xsl"; var file2 = "30.doc"; getFileExtension(file1); //returns xsl getFileExtension(file2); //returns doc  function getFileExtension(filename) {     /*TODO*/ } Would it better the community if we got compensated for posts? Even with minuscule alt coins? If we are effectively generating more traffic to Stack Exchange sites, would it become a better community if users were compensated somehow besides rep points? Even with minuscule alt coins? Short story from many years ago: the ancient, brilliant, cruel race was Earthlings How do I use the different shutter speeds my camera offers? What word could describe an operation of either importing or exporting?  X is to import and export as migration is to immigration and emigration.  Porting isn't the word I'm looking for, I don't think, but that's what I'm getting at. Cheers! Where does gravitational waves' energy go? Series $\frac{x^{3n}}{(3n)!} $ find sum using differentiation I am trying to prove that all vector spaces can be written as the direct sum of two subspaces.  My attempt: If each vector in vector space V can be uniquely written as the sum of two other vectors in V, the two vectors can be categorized into subspaces and thus V can be written as the direct sum of these subspaces. I am not sure how to show that this is true for all cases though. Edit Sorry for the confusion,to clarify I meantGiven a vector space V with a subspace W, prove that there exists a subspace W' such that the direct sum of W and W' is V.I am not sure about my proof method at all. Thank you. `--no-install-recommends` only specified packages I want to install xfce4-goodies but I don't want Midori Browser. With --no-install-recommends I don't know how to specify only Midori. I want the rest of packages. How to do that? Thanks! I am watching Susskinds's lecture , in which he introduced square angular momentum operator $L^2$, which can be written as $$ L^2=L_z^2+L_-L_++L_z $$ where $$ L_\pm=L_x\pm iL_y $$  Besides, he argued that the spectrum of $L$ can only be $m,m-1,\cdots,-m+1,-m$ in which $m$ is an integer or half-integer. If we denote $|m\rangle$ the eigenvector corresponds to eigenvalue $m$, we have $$ L_\pm|l\rangle=|l\pm 1\rangle\;\text{or}\;0 $$  In the lecture he showed that $L^2|m\rangle=m(m+1)|m\rangle$ for $m$ the highest eigenvalue, by $$ \begin{align*} L^2|m\rangle&amp;=L_z^2|m\rangle+L_-L_+|m\rangle+L_z|m\rangle\\ &amp;=m^2|m\rangle+0+m|m\rangle\\ &amp;=m(m+1)|m\rangle \end{align*} $$  Then he left an exercise to show that for any $-m\leqslant l&lt; m$, we also have $|l\rangle$ is an eigenvector of $L^2$ with eigenvalue $m(m+1)$.  In the lecture, he hinted by showing that it suffices to show that $L^2$ commutes with $L_i$ for $i=x,y,z$, which gives us $$ L^2|m-1\rangle=L^2L_-|m\rangle=L_-L^2|m\rangle=L_-m(m+1)|m\rangle=m(m+1)L_-|m\rangle=m(m-1)|m-1\rangle $$  I believe it is true since I find the   online.   However, my question is that, why the following proof is wrong.  I tried to mimic the proof for $|m\rangle$ to have that  $$ \begin{align*} L^2|k\rangle&amp;=L_z^2|k\rangle+L_-L_+|k\rangle+L_z|k\rangle\\ &amp;=k^2|k\rangle+L_-L_+|k+1\rangle+k|k\rangle\\ &amp;=k^2|k\rangle+|k\rangle+k|k\rangle\\ &amp;=(k^2+k+1)|k\rangle \end{align*} $$  which shows that $|k\rangle$ does not have eigenvalue $m(m+1)$ but $k^2+k+1$ for $k&lt;m$. Biblatex with Biber: Configuring my editor to avoid undefined citations Running the minimal example  \documentclass{article} \usepackage{filecontents} \begin{filecontents*}{\jobname.bib} @ARTICLE{example,   author  = {Other, Anthony Norman},   title   = {Some things I did},   year    = {2014},   journal = {J.~Irrep. Res.},   volume  = {1},   number  = {1},   pages   = {1-10} } \end{filecontents*} \usepackage[backend=biber]{biblatex} \addbibresource{\jobname.bib} \begin{document} Hello\cite{example}. \printbibliography \end{document}   I get the warning There were undefined references.  I have read  and know that I need to run:   LaTeX Biber LaTeX   However, my editor is only set up to run BibTeX. How do I go about setting up my editor/IDE to be able to run Biber, and how do I run the LaTeX/Biber/LaTeX cycle?  Answers (sorted alphabetically by editor name)                    Answer guidelines   Each answer should be for one editor. If the editor is cross-platform, if possible give a single answer with notes covering the minor platform variations. Please edit the question to include new answers in the 'link list' Each answer should be 'stand alone', i.e. don't say 'It's almost the same as editor Y but ...' for the editor part Instructions for 'build tools' such as arara or latexmk are welcome but should explain how to set up the editor in question as not all editors allow simple addition of arbitrary tools SQL Index Performance - ASC vs DESC On thanksgiving day a woman posted in a facebook group that her father had just passed away (left her money) and in good deed because it was thanksgiving she was offering to pay people’s debts. Well I inboxed her and she pretty much wants me to open up a bank account with First Tech Credit Union and give her my log in and password info. Ofcourse its sketchy!   So I questioned her and asked why she wanted that instead of her sending me the money directly from her bank to mine. She then responded because she wants to keep records of my debts. (She asked for proof and I sent her screenshots ONLY of my outstanding balances) I heard about the depositing checks scam so I questioned her about how she would deposit the funds and she said cash.  Her facebook page is 100% legit, I screenshotted her pics and family profiles etc. We came to an agreement that I would only accept her help if she sends me a picture of her ID before me sending this info.   She literally just wants to deposit the money to me, She isn’t asking me to send nobody money from that account or anything. Of course the account will be empty when I provide it to her. When she does deposit the money I am planning to immediately change the password and obviously stay watching my account activity while she deposits the funds.   She actually also provided pics of other accounts she funded. My question is, is this a scam? And if so how could she possibly scam me? Specially if i have her information and A pic of her ID. She is a christian lady and looks like she has a good heart, We talked about my struggles and she actually looked into why I needed to be assisted with the money. By no means was she pushy or anything. I want to believe that she just wants to help me but I am also too skeptical. If Python does not have a ternary conditional operator, is it possible to simulate one using other language constructs? Is "laic" an alternative word to the word "layperson"? I've been having problems with a blue-screening Laptop (BCCode 124), and I've been trying to track down whats causing it. (It bluescreened randomly after 5-30 minutes of running in win7). It worked in safe mode. I tried reinstalling Windows, which didn't work, so I tried to install various Linux systems which also didn't work.  The only thing working right now is the parted magic version of the ultimate boot cd.(Its a repair linux distro that runs live from ram)  I had the idea to run a bunch of stability tests to try and isolate the faulty component(s), and I wanted some input on my results.  I did different cpu stresstests for different times. No problem (temerature ~60°C sometimes peaks at 65)  I ran memtest with no errors many times.  I also did a GPU check wich is included in the ultimate boot cd - parted magic distro - no problem.  I also checked the hard drive with different tools included in parted magic - no problem there too.  Every linux system I try to install crashes when I try to install it. (It either freezes with no error (rarely happens) or I get something like this shortly after I tell it to install (tried about 20 different distros): [*] 3 photos in the dropbox  Trying to isntall windows 7 just gives a generic "there was a problem" / "an error has occured" screen with no further information.  The laptop is a Lenovo B570. Here are the detailed system specs (the ram is a 4GB kingston now) [*] the hardinfo file in the dropbox  I have 3 crashdumps from Windows wich I can not open. (visual studio says it cant open old crashdump files) [*] 3 dumps in the dropbox  Can you help me to track down the cause?  Edit: im not allowed to post more than 2 links here so here the dropboxfolder with all the things I mentioned:  [*] I know that I can update a snap package using  sudo snap refresh &lt;package&gt;   But is there a way to update all snaps, like   sudo apt dist-upgrade How to use find command with wildcard when current directory contains a match? Possible Duplicate:          I'm having some confusion with the find command.  If I type:  find . -name *.xml   or   find ./ -name *.xml   I receive a list of all the xml files in subdirectories of the current directory, UNLESS the current directory contains an xml file, in which case I get:  find: paths must precede expression: foo.xml Usage: find [-H] [-L] [-P] [-Olevel] [-D help|tree|search|stat|rates|opt|exec] [path...] [expression]   What is the correct way to search for files with wildcard when the current directory may contain a match?