Non normalisability implies uncertainty principle? The wave function $\psi(x,t)$ for a free particle assuming that the position and momentum is well defined, can be solved from the schroedinger equation, $$\frac{-\hbar^2}{2m}\nabla^2\psi+V\psi=\hat{E}\psi$$ And that wave function is $$\psi(x,t)=Ae^{i(kx−\omega{t})}$$ and also we know that this wavefunction is not normalisable. Thus we conclude that this particle has no well defined momentum (and hence energy). But uncertainty principle says the same thing. That is, particle has no well defined momentum and position. Now, my question is that is these two concepts are same? That is, non-normalisability implies uncertainty principle? or is there a different conceptual explannation about the non normalisability of the wavefunction? I think a big mistake happened to me in understanding both these concepts. pls help
is there any uncertainty on the free particle with a definite momentum $\vec p$? The probability amplitude for a free particle with momentum $\ p$ and energy $E$ is the complex wave function: $$\psi_{(\vec x , t)}=e^{i(\vec k\cdot \vec x -\omega t)}$$  is there any uncertainty on the free particle with a definite momentum $\vec p$!?
The client can do several actions per frame, for instance, requesting a movement, shooting etc. Should i send a packet to the server for each action the client performed during the frame, or should i stack them in an unique packet and send it at the end of the frame?  EDIT: i'm using Jmonkeyengine and the provided network API SpiderMonkey. Java reflection: how to get field value from an object, not knowing its class How do I find out which version and derivative of Ubuntu is right for my hardware in terms of minimal system requirements? For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements? How to identify multiple USB-serial adapters under Ubuntu 10.1 I was asked this question in an interview.  Lets say we have a correlation matrix of the form \begin{bmatrix}1&amp;0.6&amp;0.8\\0.6&amp;1&amp;\gamma\\0.8&amp;\gamma&amp;1\end{bmatrix}  I was asked to find the value of gamma, given this correlation matrix. I thought I could do something with the eigenvalues, since they should be all greater than or equal to 0.(Matrix should be positive semidefinite) - but I don't think this approach will yield the answer. I am missing a trick.  Could you please provide a hint to solve for the same? How do I put an image texture on a material in Cycles? I am creating a model of a glass and I would like to put a drawing on it (a png picture).  I know how to do it using Blender Render, but not with Cycles Render. Help :) Is it possible to reintegrate a Horcrux? If you draw two circles that are exactly the same in all aspects (location, size, etc...) except they have different colors, then the "border" of the underlying circle is showing through.  \documentclass[10pt]{book} \usepackage{xcolor} \usepackage{tikz}  \begin{document}  \begin{tikzpicture}     \fill (0,0) circle (0.1);     \fill[color=red] (0,0) circle (0.1);     \fill[color=red] (0.5,0) circle (0.1); \end{tikzpicture} \end{document}   Notice the first circle has a black "edge" around it that looks different than the 2nd circle which doesn't.   The problem is due to the fact that one is anti-aliasing both circles and the edge colors are being blended.   Is there a way to fix this but still have anti-aliasing? (basically render all the objects I need then anti-alias them properly afterwards?)  (I realize TikZ probably can't do anything about this but one doesn't know unless they ask) Is there a systematic way to obtain all conserved quantities of a system? Are Goodberries affected by the Life domain class features? Living potato clock? $L^p$ spaces and counting measure currently I am working on the following two exercises as a revision for my exam.  Let $\mu$ be the counting measure on $\mathbb N$.   Show that if $1 \le p &lt; s &lt; \infty$ then $f \in L^p$ implies $f \in L^s$ and $\|f\|_s \le \|f\|_p$. Show that if $f \in L^p$ for some $p \ge 1$ then $\lim_{s \to \infty} \|f\|_s = \|f\|_\infty$.   My attempts so far:   It is $f \in L^s$ iff $\sum_{k = 1}^\infty |f(k)|^s$ converges. Since $f \in L^p$ we know that $\sum_{k = 1}^\infty |f(k)|^p$ converges. Thus for any $\varepsilon &gt; 0$ there is $N \in \mathbb N$ s.t. \begin{align*} k \ge N \Longrightarrow |f(k)|^p &lt; \varepsilon \Longrightarrow |f(k)| &lt; \varepsilon^{1/p} \end{align*} We have $\forall k \ge N$ that $|f(k)|^s &lt; \varepsilon^{s/p}$. Originally I wanted to use the comparison test now, showing that \begin{align*} \sum_{k = N}^\infty \varepsilon^{s/p} &lt; \infty, \end{align*} but that does not work since \begin{align*} \sum_{k = N}^\infty \varepsilon^{s/p} = \varepsilon^{s/p} \underbrace{\sum_{k \ge N} 1}_{= \infty},  \end{align*} so I don't know how to go on here. Let $K := \|f\|_\infty$. We need to show that $\forall \varepsilon &gt; 0$ $\exists M \in \mathbb N$ s.t. \begin{align*} s \ge M \Longrightarrow \left|\left(\sum_{k = 1}^\infty |f(k)|^s\right)^{1/s} - K\right| &lt; \varepsilon. \end{align*} Choose $M$ s.t. $M &gt; p$. Then $s &gt; p$ and from part (i) we know that \begin{align*} \left(\sum_{k = 1}^\infty |f(k)|^s\right)^{1/s} \le \left(\sum_{k = 1}^\infty |f(k)|^p\right)^{1/p}. \end{align*} But how can I use this? What does "href" stand for in HTML? I'm trying to define a new environment that consists of a split environment inside an equation environment. But I'm getting an error. Here's what I'm doing:  \documentclass[a4paper,12pt]{article} \usepackage[brazil]{babel} \usepackage[utf8]{inputenc} \usepackage{amsmath} \newenvironment{example}{\begin{equation}\begin{split}}{\end{split}\end{equation}}  \begin{document} \begin{example}oi\end{example} \end{document}   And the error message I'm getting is:   ERROR: LaTeX Error: \begin{split} on input line 8 ended by \end{example}.   I then tried a few other cases. If I remove the splits and define example to be just equation, it runs fine. If I remove the equations and define example to be just split, I get the exact same error message.  In other words: I only get this error when split is involved. Is there a way to make this work?  EDIT: The reason I'm doing this, is because I want a convenient way to create split-equations. I know it's similar to align. I prefer split-equations because the entire line of equations gets a single number for referencing (it's even placed in the middle line). align, however, will force me to \notag each line, otherwise I get a number for each line in the equation (which tends to get messy when equations are long and numerous). It's not the end of the world, but the split-equation combination is just quicker and easier (if I can manage to define a command for it).  Alternatively, the multline environment is not appropriate either, because it doesn't let you manually align each line (like aligning the equal signs). Instead it only lets you push everything left or right.  EDIT2: I just tried this:  \newenvironment{example}{ \begin{equation}\split}{\endsplit \end{equation}}   and got this error  ERROR: LaTeX Error: \begin{equation} on input line 8 ended by \end{example}.   Which is weird, because removing \split and \endsplit entirely doesn't return any errors (so it's not equation's fault). Image data URI and SEO Do you think the use of image data URI is SEO friendly?   On the one hand saves you a HTTP request. On the other hand it really messes up your code. Especially for image files larger than 20KB or moving GIF image files of up to 200KB, the quantity of code inserted is enormous. As Googlebot reads usually from top to bottom, all data after the image data URI encoding will be harder to rank well in Google.   Consider that image data URI is not in the CSS files as they should normally be and for the time being I can use only TinyMCE editor which provides me with just two options, either insert image with the image data URI method or the traditional image link.   I would like to know which is more search engine friendly. Can I color text by using an image, so that the color isn't flat? I'm using tikz to attempt to make a book cover, and I have a "wallpaper" image that looks like leather (not that I've handled that many leather-bound books). I'm using the node command to place text over the top of it, but none of the colors I've experimented with look decent.  Can I use an image of gold-leaf as the fill/stroke for the text? Or for that matter, for the path lines as well?  I've tried googling for this, but I can't figure out a set of keywords non-generic enough to pull back useful results. I am aware that, to use a Spell Scroll, you must have the related spell on (at least one of) your spell list(s). Then, if you have the spell slot to cast it, you succeed automatically; else, you must make an ability check in order to cast it (failure resulting in the scroll being wasted).  Consider this example : A Cleric 5 / Wizard 4 finds a Raise Dead Spell Scroll. The spell is on the Cleric List, but is a fifth level spell. Considering that the cleric-wizard has fifth level slots, but can only pick up to third level cleric spells, would he have to make the ability check to successfully cast the Raise Dead in the Spell Scroll, or would he succeed automatically ? What's with the Japanese SO's stats? The only thing I need is an exact copy of an existing shapefile in the same directory with a different name.  I have tried:   arcpy.CopyFeatures_management (ORLinks, MyLinks) #ORLinks: old links, MyLinks: new links   but for some reason, I cant make it a feature layer using:  arcpy.MakeFeatureLayer_management(MyLinks, 'MyLinks')   Error Encountered:  Error: Failed to execute. Parameters are not valid. ERROR 000732: Input Features: Dataset  M:\RAIL\Rail2.0.shp does not exist or is not supported Failed to execute (MakeFeatureLayer). While learning about Random variables I came across the mean of random variable X.  The definition says that the expected value of random variable E(X) = Mean of Random variable X  I am not able to understand why is that so. Can any one please help me with it