Quantum mechanics is governed by Schrodinger's equation:  $$\hat{H}\psi=i\hbar\partial_t \psi$$  It seems that Hamiltonian acts on wave functions like a time derivative. Just out of curiosity, is there any Hamiltonian that contains time derivatives, either first order or second order?
In the time-dependent Schrodinger equation, $ H\Psi = i\hbar\frac{\partial}{\partial t}\Psi,$  the Hamiltonian operator is given by  $$\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V.$$  Why can't we consider $\displaystyle i\hbar\frac{\partial}{\partial t}$ as an operator for the Hamiltonian as well? My answer (which I am not sure about) is the following:   $\displaystyle H\Psi = i\hbar\frac{\partial}{\partial t}\Psi$ is not an equation for defining $H$. This situation is similar to $\displaystyle F=ma$. Newton's second law is not an equation for defining $F$; $F$ must be provided independently.   Is my reasoning (and the analogy) correct, or is the answer deeper than that?
zsh scripting - How do I NOT match a pattern in filename generation? My computer name in System Preferences &gt; Sharing is set to &quot;archos&quot;, but is showing as &quot;iphone&quot; on Terminal. It just started doing this after I loaded Xcode for doing iPhone development: Last login: Mon Nov  7 14:46:55 on ttys001 iphone:~ travis$   Any ideas what could be causing this? How do I start applications automatically on login? Why can't an electric field line suddenly break? My book has the following question in it as an exercise:  An electrostatic field line is a continuous curve i.e. a field line cannot have sudden breaks. Why not?  I cannot seem to be able to reason for or against this statement.  Can somebody please tell me why they can't suddenly break and if that were to happen then what will be its outcome? Is Duck/Duct tape safe to use to insulate mains wires? Question says it all really. Based in the UK so mains is 240v and 20 amps. It's a lighting circuit. How do I get a platform-dependent new line character? How do I get a platform-dependent newline in Java? I can’t use "\n" everywhere. Execute sudo without Password? Inspired by this ....  I am the sole person using my system with 12.04. Every time I issue a sudo command; the system asks for the user password (which is good in its own way).  However I was thinking; without activating the root account; how can I execute the sudo commands which will not ask for user password to authenticate.  NOTE: I want to execute sudo command without authenticating via password; only when they are executed via terminal. I don't want to remove this extra layer of security from other functions such a while using 'Ubuntu software center' or executing a bash script by drag-drop something.sh file to the terminal. algebraic element over a field Let $F$ be a subfield of a field $K$, $a$ an element of $K$.  Prove that $a$ is algebraic over $F$ iff $F[a]=F(a)$.  For the first direction I've tried this: $a$ is algebraic over $F$ $\Rightarrow$ there is a polynomail $f$ over $F$ such that $f(a)=0$ $\Rightarrow$ $1,a,a^2,...,a^m$ are linearly dependent $\Rightarrow$ $\deg(F[a])&lt;m$.    but it contains $f(a)$ so they are equal..  is that correct? about the other direction.. i simply have no clue How to understand the drawbacks of K-means K-means is a widely used method in cluster analysis. In my understanding, this method does NOT require ANY assumptions, i.e., give me a dataset and a pre-specified number of clusters, k, and I just apply this algorithm which minimizes the sum of squared errors (SSE), the within cluster squared error.  So k-means is essentially an optimization problem.  I read some material about the drawbacks of k-means.  Most of them say that:   k-means assumes the variance of the distribution of each attribute (variable) is spherical;  all variables have the same variance; the prior probability for all k clusters is the same, i.e., each cluster has roughly equal number of observations;   If any one of these 3 assumptions are violated, then k-means will fail.  I could not understand the logic behind this statement. I think the k-means method makes essentially no assumptions, it just minimizes the SSE, so I cannot see the link between minimizing the SSE and those 3 "assumptions". sudo credential caching on by default Just installed a minimal ubuntu 12.04, then installed xfce4 and xinit from the command line after first boot.  Totally vanilla installation afaik.  I'm noticing that sudo caches the password until I issue sudo -k to clear it.  This is unexpected behavior in my mind.  I've run xfce4 before and don't recall credential caching being on, nor have I experienced it in the many previous ubuntu installs I've had over the years.  Is this a new feature of Ubuntu?  Is this something that's the result of the minimal install?  Is this an xfce default that's been added recently? "At" vs. "in" before verb In a document I found the following sentence:     listeners are more accurate at understanding speech spoken in their own accent...   Would it be an error to use "in" instead of "at"?  Actually in this case "at" sounds better than "in", but in general before verb is "at" always used? There has been quite a few times that I wished I could send a message to another user on SO - not ask a question for everyone to see, but just a short message informing them of something or requesting them to do something.  Are there any plans to allow this to happen in the future?  Related: Why do I have two docks in Ubuntu desktop (with GNOME 3) after installing Dash to Dock? What's going on here? I've installed the  on Ubuntu 17.10. Everything was cool, and as I was trying to hone and tweak the look of my desktop, at some point the shortcuts bar (dock?) on the left is duplicated.  (Click image to enlarge) The default, which normally disappears with Dash to Dock, is there underneath the one that usually shows up when I install Dash to Dock. Why? I've tried to go through the options for Dash to Dock, the GNOME Tweak Tool, and the regular Ubuntu settings, but I can't figure it out. I have a problem understanding the proof of Rencontres numbers (Derangements) Scenario:   Create SymLink: C:\Data\workspaces --&gt; C:\Users\****\Documents\workspaces Navigate to C:\Data\Workspaces in explorer Click and drag the the path from the address bar onto "Quick Access" in the navigation pane.   Expected Result:   Clicking on the shortcut takes you to C:\Data\workspaces   Actual Result:   Clicking on the shortcut takes you to C:\Users\****\Documents\workspaces   How do you make it so that the shortcut points to the correct path. (the SymLink)  Command Used to create the SymLink:  mklink /D C:\Data\workspaces C:\Users\****\Documents\workspaces   Updated with pictures:  Please note the workspaces symlink inside C:\Data:    When I double-click on the symlink it works correctly. (note the address bar.    When i pin it to the Quick access bar, however, it uses the address that the symlink points to and NOT the symlink address. IBM Slack links broken Does anyone know where I can find working Slack invite links to any of IBM's Slack pages? The Slack links on  are all broken. Thank you. During Winter Bash, users can earn hats. But sometimes it seems that a hat was awarded even though its requirements weren't (yet) met, or vice versa.  What could be the reason for this? As discussed here:  offering actual money as a bounty sets the wrong incentives. However I would suggest giving users the ability to pay with money for offering a bounty regardless of their reputation. The bounty would still count as reputation for the receiving user but would not be discounted from the paying user's reputation. Install Java JDK and JRE on Debian 8 I installed Debian 8, I would like to install Java JRE and JDK. I use  and it works.  But, I am afraid because it's a script hosted in a repository. I would like to understand why it doesn't work when I put the extract of  in /usr/java/jre1.8.0_73 directory as . I added the path variable with PATH=/usr/local/jdk1.8.0/bin:$PATH export PATH as explained in  but it doesn't work.  Even if I try to install OpenJDK, the package isn't found. I don't understand why it's so complicated to install Java on Debian; it is very simple on Ubuntu. I would like someone give me step-by-step instructions to install it. Invert Color Ramp in QGIS