Stationary State of Quantum Mechanics
How will a particle with energy less than $V_{\rm min}$ behave?
Let $f(z)=\frac{1}{(z-1)(z-2)}$ and $g(z)=\frac{z}{(z-1)(z-2)}$. Let $\gamma$ be the circle of radius 4 centered at the origin and traveled once in the counterclockwise direction. Let $A=\{ z \in \mathbb{C}: |z|&gt;3 \}$  1) I need to show there is no analytic function $G: A \to \mathbb{C}$ such that $G'(z)=g(z)$ for all $z$ in $A$.   2) I also need to show that there is an analytic function $F:A \to \mathbb{C}$ such that $F'(z)=f(z)$ for all $z$ in $A$.  Do I have to integrate to find such function? Mob Arena - Mob vs. Mob I want to make an arena where mobs will fight each other and a player can bet on one side or the other. For example: There are 2 skeletons in dyed armor; red and blue. Each color representing a team. When they spawn I want them to fight each and then when one dies I want it to announce which team is the winner and give the player the "money" due. I'm just not sure how to get the skeletons to attack each other without a player instigating it. Ambiguity in Negation: "John did not come because of the rain" Why do I get 'HDIO_GET_IDENTITY failed' message when booting with external usb hard drive? I've installed Ubuntu 11.10 on an external USB (2.0) Hard Drive (/dev/sdb1) but when Ubuntu starts I get a message that says:     ata_id[279]: HDIO_GET_IDENTITY failed for '/dev/sdb': Invalid argument   where I made a mistake? The first HD contains Windows 7 (the official OS of my packard bell notebook). Why Was Peter Pettigrew Sorted To Gryffindor? Using expect for inputting commands Heres the thread I'm bouncing off of:   So I'm trying to run this command: cd /etc/openvpn/easy-rsa; . ./vars; ./build-key username  However, after running that command, I need to input nothing [just press enter] 10 times, and press y twice. The user on the last thread suggested I use except, but I couldn't get it working. Here are the questions it asks:  root@suffice-vpn:/etc/openvpn/easy-rsa# ./build-key usernamtest Generating a 2048 bit RSA private key ..................+++ ........+++ writing new private key to 'usernamtest.key' ----- You are about to be asked to enter information that will be incorporated into your certificate request. What you are about to enter is what is called a Distinguished Name or a DN. There are quite a few fields but you can leave some blank For some fields there will be a default value, If you enter '.', the field will be left blank. ----- Country Name (2 letter code) [US]: State or Province Name (full name) [NY]: Locality Name (eg, city) [Merrick]: Organization Name (eg, company) [IceWare]: Organizational Unit Name (eg, section) [IceWare]: Common Name (eg, your name or your server's hostname) [usernamtest]: Name [server]: Email Address [iceware@programmer.net]:  Please enter the following 'extra' attributes to be sent with your certificate request A challenge password []: An optional company name []: Using configuration from /etc/openvpn/easy-rsa/openssl-1.0.0.cnf Check that the request matches the signature Signature ok The Subject's Distinguished Name is as follows countryName           :PRINTABLE:'US' stateOrProvinceName   :PRINTABLE:'NY' localityName          :PRINTABLE:'Merrick' organizationName      :PRINTABLE:'IceWare' organizationalUnitName:PRINTABLE:'IceWare' commonName            :PRINTABLE:'usernamtest' name                  :PRINTABLE:'server' emailAddress          :IA5STRING:'iceware@programmer.net' Certificate is to be certified until Jan 14 18:27:48 2026 GMT (3650 days) Sign the certificate? [y/n]:y   1 out of 1 certificate requests certified, commit? [y/n]y   As you can see, I press enter 8 times initially [to keep the default input] and then press enter another 2 times to skip the optional commands. Then, I need to press y twice. How can I automate this? I need to have this all happen in one command. Any suggestions? Thanks in advance. 1.  Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an explanation that I need some help with: that the de Broglie wavelength and the wavelength of an elastic wave do not show similar properties under a Galilean transformation. He basically says that both are equivalent under a gauge transform and also, separately by Lorentz transforms. This, accompanied with the observation that $\psi$ is not observable, so there is no "reason for it being real". Can someone give me an intuitive prelude by what is a gauge transform and why does it give the same result as a Lorentz tranformation in a non-relativistic setting? And eventually how in this "grand scheme" the complex nature of the wave function becomes evident.. in a way that a dummy like me can understand.  2.   A wavefunction can be thought of as a scalar field (has a scalar value in every point ($r,t$) given by $\psi:\mathbb{R^3}\times \mathbb{R}\rightarrow \mathbb{C}$ and also as a ray in Hilbert space (a vector). How are these two perspectives the same (this is possibly something elementary that I am missing out, or getting confused by definitions and terminology, if that is the case I am desperate for help ;)   3.   One way I have thought about the above question is that the wave function can be equivalently written in $\psi:\mathbb{R^3}\times \mathbb{R}\rightarrow \mathbb{R}^2 $ i.e, Since a wave function is complex, the Schroedinger equation could in principle be written equivalently as coupled differential equations in two real functions which staisfy the Cauchy-Riemann conditions. ie, if $$\psi(x,t) = u(x,t) + i v(x,t)$$ and $u_x=v_t$ ; $u_t = -v_x$ and we get $$\hbar \partial_t u  = -\frac{\hbar^2}{2m} \partial_x^2v + V v$$ $$\hbar \partial_t v  = \frac{\hbar^2}{2m} \partial_x^2u - V u$$ (..in 1-D) If this is correct what are the interpretations of the $u,v$.. and why isn't it useful. (I am assuming that physical problems always have an analytic $\psi(r,t)$). First time using bevel tool, doesn't bevel evenly. What am i doing wrong? First off I'll let you know I'm a total noob at blender I've used 3ds Max up until this point, but the company I'm working for at the moment needs me to use blender so I'm trying to make the transition over.  Literally all I'm making at the moment is a simple book and cannot understand how the bevel tool isn't working similar to how the chamfer tool would in 3ds Max.  I want a nice curved edge for the spine of the book however when I press control + B and try to bevel it bevels the edge unevenly with the new bevel pushing forward.    Is there a way I can get it to bevel evenly like it does in Max? Divergence as transpose of gradient? In his online lectures on Computational Science, Prof. Gilbert Strang often interprets divergence as the "transpose" of the gradient, for example  (at 32:30), however he does not explain the reason.  How is it that the divergence can be interpreted as the transpose of the gradient? Purpose: Construct a 95% confidence interval for $\theta$.   A common strategy is to construct a confidence interval for $\log(\theta)$ and then exponentiate.  Why is it valid?   My concern is that $E(\log(\theta)) \neq \log(E(\theta))$ and $Var(\log(\theta)) \neq \log(Var(\theta))$...   Do people use this back transformation because it has proven to work fine? What about other transformations (e.g. logit)? Estimating the most important features in a k-means cluster partition How can I switch between starting a coroutine vs running the routine all at once? I'm generating a level, and I have an optional delay to show the steps level generation one by one.  If my generationDelay boolean is true, I want to use StartCoroutine to spread the generation out over time. If it's false, I want to call the same method but without StartCoroutine.  The problem is that the method is type IEnumerator.  I can make two methods one type of IEnumerator and one not. But I wonder if there is a way to use one method.  In the first script top i did:  public bool generationDelay = false;   Then in a method:  private void BeginGame()     {         mazeInstance = Instantiate(mazePrefab) as Maze;          if (generationDelay == true)         {             StartCoroutine(mazeInstance.Generate(generationDelay));         }         else         {             mazeInstance.Generate(generationDelay);         }     }   Then the other script where the method Generate is: In the top:  public float generationStepDelay = 0.01f;   Then the method Generate:  public IEnumerator Generate (bool generationDelay) {          if (generationDelay == true)             WaitForSeconds delay = new WaitForSeconds(generationStepDelay);         cells = new MazeCell[size.x, size.z];         List&lt;MazeCell&gt; activeCells = new List&lt;MazeCell&gt;();         DoFirstGenerationStep(activeCells);         while (activeCells.Count &gt; 0) {             yield return delay;             DoNextGenerationStep(activeCells);         }     }   I'm getting an error on the line:   WaitForSeconds delay = new WaitForSeconds(generationStepDelay);      "Embedded statement cannot be a declaration or labeled statement"   And an error on the line:  yield return delay;      "The name 'delay' does not exist in the current context"   The reason I want to use a bool variable is that when i'm using StartCoroutine it's kind of slow, even if I change the value of generationStepDelay to 0 it's kind of slow. And if I'm not using StartCoroutine and not using the Generate method as IEnumerator it will work fast.  So i wonder what should I do and how? How to explain the long lifetime of Rydberg atoms with Fermi golden rule? Install apt package in ubuntu 12.04 I have mistakenly removed the default package APT from my system .  When I run command locate apt-get, I get below output:  /home/jeet/apt-get /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/cmdline/apt-get.cc /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/doc/apt-get.8.xml /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/doc/de/apt-get.de.8 /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/doc/fr/apt-get.fr.8 /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/doc/ja/apt-get.ja.8 /home/jeet/Downloads/apt-get /home/jeet/Downloads/apt-get.8.gz /usr/share/bash-completion/completions/apt-get /usr/share/bash-completion/completions/slapt-get   If I run ls | grep apt-get, then I won't get any output.  Can anybody please advice how to recover apt package or install it from start? If you finish a world without fighting the Broodal, can you still fight them later? I've just seen that in a speedrun: If you collect enough moons to move on to the next world, and cash them in at the ship, the broodal ship just leaves.  Does that mean that the Broodal fight wont happen, so you missed the triple moon it gives? Or if you go to the arena, even without the ship you will have the fight happen?  Clip where this happens : Is it bad to marinate meat for too long? From my experience it is always best to marinate meat for a decent amount of time, so the meat can "soak" up the marinade and be more flavourful.  However, I came across this recipe here:   In the directions, it says: Add pork and marinade for a minimum of 6 hours or overnight, but no longer than 12 hours.  I was wondering, why does it say "no longer than 12 hours"? Isn't it good to let meat marinate for as long as possible?  Thanks. Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots Showing that $\frac{z^n}{1+z^{2n}}$ is real for $|z|=1$. How can I escape white space in a bash loop list? I have a bash shell script that loops through all child directories (but not files) of a certain directory.  The problem is that some of the directory names contain spaces.    Here are the contents of my test directory:  $ls -F test Baltimore/  Cherry Hill/  Edison/  New York City/  Philadelphia/  cities.txt   And the code that loops through the directories:  for f in `find test/* -type d`; do   echo $f done   Here's the output:   test/Baltimore test/Cherry Hill test/Edison  test/New York City test/Philadelphia   Cherry Hill and New York City are treated as 2 or 3 separate entries.  I tried quoting the filenames, like so:  for f in `find test/* -type d | sed -e 's/^/\"/' | sed -e 's/$/\"/'`; do   echo $f done   but to no avail.  There's got to be a simple way to do this.    The answers below are great.  But to make this more complicated - I don't always want to use the directories listed in my test directory.  Sometimes I want to pass in the directory names as command-line parameters instead.  I took Charles' suggestion of setting the IFS and came up with the following:  dirlist="${@}" (   [[ -z "$dirlist" ]] &amp;&amp; dirlist=`find test -mindepth 1 -type d` &amp;&amp; IFS=$'\n'   for d in $dirlist; do     echo $d   done )   and this works just fine unless there are spaces in the command line arguments (even if those arguments are quoted).  For example, calling the script like this: test.sh "Cherry Hill" "New York City" produces the following output:   Cherry Hill New York City Where can I get a Master Ball? I remember in previous generations that finding a Master Ball would typically come after a major Boss fight. You could have also gotten through some form of lottery (I think this was in Pearl).  If anything, where and when will I be able to find Master Balls in Pokemon X&amp;Y?