$\langle p | x \rangle=e^\frac{ipx}{\hbar}$ can pretty easily be derived from wave mechanics. But how can it be derived without resorting to it? I've seen it be derived from the translation operator $\hat T$. It is shown that for an infinitesimal displacement $\epsilon$ the translation operator in the position eigenbasis is: $$\langle x |\hat T |\psi\rangle=\left( 1+\dfrac{\partial}{\partial x}\right)\langle x | \psi\rangle=\left( 1+\dfrac{\partial}{\partial x}\right)\psi_x$$ In which $\psi_x$ is the state vector's representation in position space, such that $$|\psi\rangle=\int^{\infty}_{-\infty}\psi_x |x\rangle dx$$ And it then assumes that because momentum generates translation, $\frac{\partial}{\partial x}=\frac{i}{\hbar}\hat p$.  Now this leaves me rather unsatisfied. Is there any way to prove the form of the momentum operator, and from it prove $\langle p | x \rangle=e^\frac{ipx}{\hbar}$ using, for example, the matrix representation of quantum mechanics?
I'm curious whether I can find the overlap $\langle q | p \rangle$ knowing only the following:   $|q\rangle$ is an eigenvector of an operator $Q$ with eigenvalue $q$. $|p\rangle$ is an eigenvector of an operator $P$ with eigenvalue $p$. $Q$ and $P$ are Hermitian. $[Q,P] = i \hbar$.   I'm asking because books and references I've looked in tend to assume that $Q$ is a differential operator when viewed in the $P$-basis, then show that it satisfies the commutation relation. (I haven't read one yet that proves that the form given for $Q$ is the only possible one.) I've heard, though, that we can work purely from the hypothesis of the commutation relation and prove the properties of $Q$ and $P$ from it.
Evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle I need to evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle.    Attempt: Let $\gamma(t) = e^{it} $ where $t \in [0,2 \pi]$. How can I get rid of the absolute values in the differential? CBC-MAC Padding weaknesses Traverse a list in reverse order in Python Why don't we consider centrifugal force on a mass placed on earth? Let us say a block of mass is placed on the surface of earth. Then while drawing the forces on that body, we say:   Force $F = mg$ acting towards the center of Earth. Normal reaction $N$ offered by the surface of Earth.   If no other forces are acting, we say $F=N$. But what about the centrifugal force $m\omega^2R$ . Why don't we ever bring that into picture? What am I missing? How do I kill entities at y=65? Potions can survive at y=65  One potion was thrown into the void, but instead of being killed, it just lingered there.  Any ideas to kill it? I can't just run /kill @e[type=!player,tag=test1]  (yes, the tag of the entity is indeed test1 ) Can not find the tag library descriptor for “http://java.sun.com/jsp/jstl/core” I'm considering taking a loan on my 401k in order to pay off and close 2 credit cards.  I have approximately 30 years until I consider retiring.  The amount of the loan will be $1700 which is less then 20% of my current 401k balance.  I will continue to put 9% of my paycheck into a Roth 401k, and my employer matches 9%.  The loan will be paid back at 3.25% (to myself) and does have $183 in fees.  There are 2 cards I will pay off and close if I follow through with this plan.  One card is 17.9% interest with roughly a $650 balance.  The other is 23% (ish) with roughly a $1,025 balance.  Both of these cards do have an annual fee associated with them, I used them to rebuild my credit and have a newer, lower interest, no fee card that I will keep active for emergencies.  Would it be advantageous for me to pay off these two credit cards and cancel them with a 401k loan? I'm in a freshmen level physics class now, so I don't know much, but something I heard today intrigued me. My TA was talking about how at the research facility he worked at, they were able to accelerate some certain particle to "99.99% the speed of light". I said why not 100%, and I didn't quite understand his explanation, but he said it wasn't possible. This confused me. Since the speed of light is a finite number, why can we go so close to its speed but not quite?  Edit: I read all the answers, and I think I'm sort of understanding it. Another silly question though: If we are getting this particle to 99.99% the speed of light by giving it some sort of finite acceleration, and increasing it more and more, why cant we increase it just a little more? Sorry I know this is a silly question. I totally accept the fact we cant reach 100%, but I'm just trying to break it down. If we've gotten so close by giving it larger and larger acceleration every time, why cant we just supply it with more acceleration? And how much of a difference is there between 99.99% the speed of light, and the speed of light? (I'm not really sure if "difference" is a good word to use, but hopefully you get what I'm asking). Find all $x$ such that $x^6 = (x+1)^6$. Find all $x$ such that $$x^6=(x+1)^6.$$   So far, I have found the real solution $x= -\frac{1}{2}$, and the complex solution $x = -\sqrt[3]{-1}$.  Are there more, and if so what/how would be the most efficient find all the solutions to this problem? I am struggling to find the rest of the solutions. Java Serialization with non serializable parts I have:  class MyClass extends MyClass2 implements Serializable {   //... }   In MyClass2 is a property that is not serializable. How can I serialize (and de-serialize) this object?  Correction: MyClass2 is, of course, not an interface but a class. How is Clan War Map position determined? Linear independence of $\sin(x)$ and $\cos(x)$ In the vector space of $f:\mathbb R \to \mathbb R$, how do I prove that functions $\sin(x)$ and $\cos(x)$ are linearly independent. By def., two elements of a vector space are linearly independent if $0 = a\cos(x) + b\sin(x)$ implies that $a=b=0$, but how can I formalize that? Giving $x$ different values? Thanks in advance. I've read a lot of conflicting advice on whether it's advisable to store eggs in the refrigerator. The case against seems twofold: (1) that eggshells are porous, and eggs can take on unwelcome flavours, or even spoil faster in the fridge, and (2) that cooking with cold eggs can be problematic. But lots of people refrigerate eggs through perceived necessity.  Do eggs last longer in the fridge, and is the shelf life gain worth it? Or should I just stick them in the cupboard? This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, including more unit test resources, navigate to the  tag.  This canonical question is intended to address several classes of common questions by providing a quick summary and links to comprehensive resources:   How is code coverage obtained and calculated? How do I increase my coverage?  Why can't I cover these lines? Why isn't the body of my loop or conditional statement covered? Is there a way to force a line break inside a math mode text?  My example:  \[   \underbrace{....}_\text{Some long text that should be multiline} \]   Trying  \text{Some long text that\\ should be multiline}   Didn't do the trick. Integral $\int\!\sqrt{\cot x}\,dx $ How to use iSight webcam without activating the green light? Recently a the Dutch government advised to put a tape on your webcam to prevent hackers from taking pictures and video using your device ().  The build in iSight camera in Apple laptops have a green light next to the camera, this light turns green when you use the camera.  Is it possible to use the camera without the activation of the green light? Personally I think the green light turns on when the sensor requires power and this is hardwired in the hardware. Am I wrong?  I have found similar questions on stackexchange, but I found non that answer this specific question. I wasn't forcing myself to say anything, or/nor trying to be funny.   "Or" sounds more grammatically correct to me. But "nor" has more Google results. So I'm confused. Just beginning to learn quantum mechanics and my textbook says that all pure eigenstates of the Schrodinger equation ( with a specified potential function) have a zero standard deviation for the expectation values of energy.So every measurement of the energy yields a fixed value. I've also read that pure eigenstates are physically realisable solutions in some situations ( like the infinite potential well). But wouldn't that violate the uncertainty principle? the standard deviation in expectation of energy is zero and hence $$ΔE~Δt=0.$$ Where am I going wrong? Also could someone also give me an insight as to what uncertainty in time even means? I haven't been able to grasp that concept clearly yet. Proper Installation of Kali linux tools in Ubuntu I think everyone has known - we need to install katoolin to use Kali Linux Tools on Ubuntu. Before did anything I had looked through the internet and also found out these solutions: ,   So here are my steps:  apt-get install git git clone https://github.com/LionSec/katoolin.git &amp;&amp; cp katoolin/katoolin.py /usr/bin/katoolin chmod +x  /usr/bin/katoolin sudo katoolin   Then, to add Kali Linux repositories and update them, I selected option 1 from the katoolin Menu  Then, to view the available categories and install all available tools, I selected option 2 from the main menu of katoolin and then pressed 0.   But after that I got this:    What do you want to do ?>    1) Add Kali repositories & Update  2) View Categories 3) Install classicmenu indicator 4) Install Kali menu 5) Help   kat > 2  ************************** All Categories **************************  1) Information Gathering                      8) Exploitation Tools 2) Vulnerability Analysis                     9) Forensics Tools 3) Wireless Attacks                           10) Stress Testing 4) Web Applications                           11) Password Attacks 5) Sniffing & Spoofing                        12) Reverse Engineering 6) Maintaining Access                         13) Hardware Hacking 7) Reporting Tools                            14) Extra  0) All   Select a category or press (0) to install all Kali linux tools .  Furthermore, I got an error in Software Updater - it didn't let me do anything. Ubuntu just hung up. I solved this problem by deleting kali linux repositories in katoolin and then in Software Updater.  Does anyone know how to install Kali Linux tools in Ubuntu 16.04 in a proper way?