Commutator of Hamiltonian and momentum
Why can't $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?
Prove Borel Measurable Set A with the following property has measure 0. This question is exercise 4.10 of Richard F. Bass's Real Analysis for Graduate Students, 2nd edition.  Let $\epsilon \in (0,1)$, let $m$ be Lebesgue measure, and suppose $A$ is Borel Measurable subset of $\mathbb R$. Prove that if $$ m(A\cap I)\leq (1-\epsilon)m(I)$$  for every interval $I$, then $m(A)=0$.  Collection of my thoughts  1. Try to prove by contradiction, suppose $m(A)=a&gt;0$ Borel Measurable Set satisfies the condition given. A property of any Borel Measurable Set on $\mathbb R$ is $A$ contains a closed set $F$ and is contained in open set $O$, and the measure of $F$ and $O$ can be arbitrarily close to $a$. 2. Obviously $A$ contains no interval, but it does not lead to contradiction, because we can find an example of $m(A)&gt;0$ that contains no interval(fat Cantor Set(remove middle 1/4 each time) has measure $1/2$ and contains no interval).  2'. For fat Cantor Set $C$ and given $\epsilon&gt;0$ how could we construct an interval I satisfies $m(C \cap I)&gt;(1-\epsilon)m(I) ?$   Maybe try to write Borel measurable set as countable union/intersection of intervals.   I'm stucked here and will appreciate any help, some examples/special case will be great too. "Eat" is to "feed" as "drink" is to what? For all $x,y\in\mathbb{R}$   define that $x\equiv y$   if $x^{2}=y^{2}$  . Then $\equiv$  is an equivalence relation on $\mathbb{R}$  , there are infinitely many equivalence classes, one of them consists of one element and the rest consist of two elements.  Solution  True. To show that \equiv  is reflexive we need to show that \forall x\in\mathbb{R}  :x=x.  Let x\in\mathbb{R}  , x\equiv\mbox{\ensuremath{x}}  if x^{2}=x^{2},   which is obvious.  [x]  ={y\in\mathbb{R}  |x\equiv y}  =[0]={y\in\mathbb{R}|0\equiv y}={0}  . Hence y^{2}  =0^{2}   =0   which implies that y=0  . How can reincarnated souls be summoned using Edo Tensei? Quoting ,     Reincarnation is the philosophical or religious concept that an aspect of a living being starts a new life in a different physical body or form after each biological death. It is also called rebirth or transmigration, and is a part of the Saṃsāra doctrine of cyclic existence.   Then, since Ashura has reincarnated into Naruto, and Indra into Sasuke, how can Uchiha Madara and Senju Hashirama (their previous reincarnation) be summoned using Edo Tensei? The Boolean modifier is not working Highlighting or coloring certain words / substrings appearing in a larger string Why the "service --status-all | grep mysql" get many unrelated result? I'm trying to prove that $(ma, mb) = $|$m$|$(a, b)$ , where $(ma, mb)$ is the greatest common divisor between $ma$ and $mb$. My thoughts: If $(ma, mb) = d$ , then $d$|$ma$ and $d$|$mb$ → $d$|$max + mby$ → $d$|$m(ax+by)$. This implies that $d$|$m$ or $d$|$(ax+by)$. This is the same as  $d$|$m$ or $d$|$a$ and $d$|$b$, so $d$|$m$ or $d$|$(a,b)$. This is the same as $d$|$m|$ or $d|(a,b)$, so $d$|$|m|(a,b)$. I don't know what to do. Run as a different user on a shortcut How do I run as a different user on a shortcut in Windows 7?   On Windows XP, I had the ability to mark a shortcut as being run by a different user, so that every time I ran it it would prompt me for a username/password. This let me have two shortcuts for things like , one for my normal account and one for my domain administrator account which has access to production servers.  I can get to the 'Run as different user' option with Shift + right-click, but I can't see an option anywhere that would let me mark the shortcut as doing this every time. Learning Regular Expressions As much as I have tried, it doesn't seem possible to use separate labels when using a casesconstruction (from the amsmath package).  Ideally, I would like to be able to write something like  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} f(x)=\begin{cases}   1&amp;x\geq0\label{positive}\\   0&amp;x&lt;0\label{negative} \end{cases} \end{equation} \end{document}   and later refer to both cases at different places. What would be the best way to achieve this result? Can $\frac{\sqrt{3}}{\sin20^{\circ}}-\frac{1}{\cos20^{\circ}}$ have two values? I just started playing Overwatch (played a few games during open beta, but wasn't able to play much). I'm enjoying Mercy, but who (in a group situation) should be getting the damage buff? Additionally, when my team splits up, who should I follow to support? derivative of a determinant of matrix Let $A,B\in M_{n\times n}(\mathbb{R})$, prove that $$(\frac{d}{dt}\det(A+tB))_{t=0} = Tr(cof(A)^{T}\cdot B), $$ where $cof(A)$ is the cofactor matrix of $A$. I tried expanding it using row expansion, but it gets messed up. Any help? How to access the Keyboard Layout Options in 13.10+ What happens when you plug two sides of a cable to a single networking device? What is likely to happen when you plug two ends of a network cable to a single switch/router? Will this create problems on the network, or just be ignored? How to suppress scientific notation when printing float values? Here's my code:  x = 1.0 y = 100000.0     print x/y   My quotient displays as 1.00000e-05.  Is there any way to suppress scientific notation and make it display as 0.00001? I'm going to use the result as a string. Can I use the Stack Exchange concept in my own sites? I am thinking of making a site which will have a forum. I already have a lot of users (in an old forum, which I want to renew).  I like the Stack Exchange concept (voting, reputation, etc).  Can I build one of my own on my site? (I don't intend to copy any source code, just the concept itself.)  Is the concept patented or otherwise legally protected, or is it free to use? I need to get rid of the GNOME Desktop Environment which has been installed by default when I updated my pc from 15.10 to 16.04.  After a while, I found myself not only with GNOME DE, but also with Cinnamon alongside (in the login screen, I could choose at least five or six DE!)  Now I am using Unity, and I'm happy with that, and I successfully uninstalled Cinnamon, but now I'm afraid that after uninstalling GNOME I will mess up the Unity DE, since I see many packages running in unity with the packagename starting with gnome-... Would someone mind to help me? Thx in advance How to get the type of T from a member of a generic class or method Let's say I have a generic member in a class or method, like so: public class Foo&lt;T&gt; {     public List&lt;T&gt; Bar { get; set; }          public void Baz()     {         // get type of T     }    }  When I instantiate the class, the T becomes MyTypeObject1, so the class has a generic list property: List&lt;MyTypeObject1&gt;. The same applies to a generic method in a non-generic class: public class Foo {     public void Bar&lt;T&gt;()     {         var baz = new List&lt;T&gt;();                  // get type of T     } }  I would like to know what type of objects the list of my class contains. So what type of T does the list property called Bar or the local variable baz contain? I cannot do Bar[0].GetType(), because the list might contain zero elements. How can I do it?