I want points for practicing triangulation algorithms.  Just points with coordinates [X,Y] and elevation [Z] of real world terrain.  I can use Google Maps Elevation API, but there is no method how to get only significantly terrain points.
Is there any freely available pointcloud data?   I'm especially interested in dense clouds of small areas(5m to 100m radius) but anything else would be fine too.   I've found that these pages have very nice and easy to access point cloud data.
I am going through Shankar's Principles of Quantum Mechanics and am having trouble finding the free particle propagator $U(t)$ that satisfies $$\lvert\psi (t)\rangle = U(t)\lvert\psi (0)\rangle$$ due to the degeneracy of the $E$ eigenkets. Shankar says that if the Hamiltonian has degenerate eigenvalues, we change the propagator equation from $$U(t) = \sum_{E} \lvert E\rangle\langle E\rvert e^{-iEt/{\hbar}}\tag{4.3.13}$$ to $$U(t) = \sum_{E} \sum_\alpha \lvert E, \alpha\rangle\langle E, \alpha\rvert e^{-iEt/\hbar} $$ where $\lvert E, \alpha \rangle $ are the orthonormal eigenkets for the $E$ eigenspace. This makes sense to me, because it seems like whenever we deal with degeneracy to use a projection. He also says for a Hamiltonian with no degeneracy to change the sum into an integral, so I imagine that for a Hamiltonian with a continuous, degenerate spectrum we would have this propagator: $$ U(t) = \sum_\alpha\int_\Re dE\lvert E, \alpha\rangle\langle E, \alpha\rvert e^{-iEt/\hbar}$$  I tried applying this to the free particle and had some trouble. In the book, after solving for the eigenkets and eigenvalues, $\lvert E\rangle = \lvert p\rangle$ and $p = \pm\sqrt{2mE}$, he chooses the propagator as a function of the momentum eigenvalues $p$ so that $$U(t) = \int_\Re dp\lvert p\rangle\langle p\rvert \exp(-ip^2t/2m).\tag{5.1.9}$$ I understand how he got to this, but I'm having some trouble because this doesn't appear to be the same expression that I have above. Splitting the integral up, we have $$U(t) = \int_{-\infty}^0dp\lvert p\rangle\langle p\rvert \exp(-ip^2t/2m) + \int_0^\infty dp\lvert p\rangle\langle p\rvert \exp(-ip^2t/2m)$$ The left integral can changed to an integral over $-p$, and the bounds switch from $0$ to $\infty$ such that: $$U(t) =  \int_{0}^\infty d(-p)\lvert -p\rangle\langle -p\rvert \exp(-ip^2t/2m) + \int_0^\infty dp\lvert p\rangle\langle p\rvert \exp(-ip^2t/2m)$$ Now we can substitute and interchange $\lvert p\rangle = \lvert E, + \rangle$,  $\lvert -p\rangle = \lvert E, - \rangle$, $E = p^2/2m$, and $dp = \pm mdE/\sqrt{2mE}$ to get: $$U(t) = \sum_{\alpha = \pm} \int_0^\infty dEm/\sqrt{2mE}\lvert E, \alpha\rangle\langle E, \alpha\rvert e^{-iEt/\hbar}. $$ This is the result that we are asked to prove in Exercise 5.1.1. Why is this not the same as the first expression for the propagator? Where did the extra $ m/\sqrt{2mE} $ come from? Am I just wrong in assuming that that is the general expression for a Hamiltonian with continuous and degenerate eigenvalues? How to change permission external hard drive in ubuntu 12.04 I want to copy any file to my external hard drive. But always when I tried to do this I have next output:  cp: cannot create regular file /media/NameOfCard/[file]' : Read only file system  I also tried:  sudo chmod -R 775 /media/NameOfCard sudo chmod -R 777 /media/NameOfCard   But the same effect - ... Read only file system  Update:   After mount I have next output:  nazar_art@nazar-desctop:~$ mount /dev/sda1 on / type ext4 (rw,errors=remount-ro) proc on /proc type proc (rw,noexec,nosuid,nodev) sysfs on /sys type sysfs (rw,noexec,nosuid,nodev) none on /sys/fs/fuse/connections type fusectl (rw) none on /sys/kernel/debug type debugfs (rw) none on /sys/kernel/security type securityfs (rw) udev on /dev type devtmpfs (rw,mode=0755) devpts on /dev/pts type devpts (rw,noexec,nosuid,gid=5,mode=0620) tmpfs on /run type tmpfs (rw,noexec,nosuid,size=10%,mode=0755) none on /run/lock type tmpfs (rw,noexec,nosuid,nodev,size=5242880) none on /run/shm type tmpfs (rw,nosuid,nodev) /dev/sdb1 on /media/sdb1 type vfat (rw) binfmt_misc on /proc/sys/fs/binfmt_misc type binfmt_misc (rw,noexec,nosuid,nodev) gvfs-fuse-daemon on /home/nazar_art/.gvfs type fuse.gvfs-fuse-daemon (rw,nosuid,nodev,user=nazar_art)   Any suggestions?   How to solve this trouble and let permission to copy and delete files to hard drive? Wear a hat multiple times? Illustrator: Is there an efficient and accurate way to join two circles by their tangents (and keep it editable)? It's easy to join two circles if they are the same size and horizontal/vertical, into a pill shape:    If the circles are at an add angle then it's still possible but you can no longer rely on smart guides.     You can add lines roughly where the tangents should be and then use the scissors tool on the circles, cut out the inner area and then join the two crescents into one shape.    Is there a better way to do this? Is there a way to do this that is still editable afterwards too?  There are some other questions that cover the same area as this but don't cover editability or joining circles that are not in line with each other (where smart guides can't help). Nominate for Reopening Shows Duplicate Message Boxes It seems syntax highlighting is not enabled on every SE site, but later on turns out to be rather advantageous. As an example,  may not have sounded like needing it, yet there is , and I think it's justified since many answers have code in them, e.g. JS for InDesign scripts, some GREP-regex and (rather obviously) HTML and CSS. While I'd appreciate having syntax highlighting activate on that specific site (so please upvote ), this question is more general about two points:   Why is syntax highlighting disabled on some sites at all? Are the additional resource costs really so high? Couldn't caching improve that then? How to actually proceed when it should become activated on a specific site? It seems feature requests on the specific meta site are not exactly handled quickly (the request mentioned above is from 2013!), and also appear overkill for a simple "please switch that site's config bool for syntax highlighting". Is the universe really "fine-tuned for life"? I understand what is meant when we say , but I've seen it claimed it's is fine tuned "for life". Is it?  When I look at known or even speculated life in our universe, I see life clinging to a tiny crumbs separated by vast voids. Our life needs baryonic matter, only 5% of the universe. Its density is $10^{-30}  g/cm^3$, but it clumps together leaving vast voids between the clumps. 99% is in stars and black holes and nebula utterly inhospitable to known life.  That leaves the parts "fine tuned for life" to be 0.05% of the universe. The planets, asteroids, and comets seem like just debris separated by  than the life-sustaining clumps preventing life from spreading.  Even that seems to be used very inefficiently. Life requires the energy of a star, but it's spewed out in all directions. We only receive a tiny fraction of it. Similarly, life requires heavier elements created in supernova, but these are also spewed out in all directions. And it took billions of years to develop a being capable of asking "is the universe fine tuned for life?"  It seems like we live on the crumbs of creation warmed by a rounding error of the heat from our star. Taking this view, the universe appears extremely inhospitable to life. It could be a lot better tuned.  Is it that the universe is fine-tuned for life? Or is it that the universe is so large and life requires such an infinitesimal fraction of the universe that it's a near guarantee were we to roll the dice again that some crumb, maybe not even baryonic matter, could develop something complex enough to ask "why is the universe fine tuned for life"? Am I just restating the weak anthropic principle?  I understand this is straying into philosophy. If that's off topic, are my  physical assumptions correct? Google chrome is reading characters backwards Deleted users who created a synonym are listed as "anon" in the tag synonyms list While browsing the  I came across the synonym [vote-to-close] -&gt; [closing] in which the creator is listed as &quot;anon&quot; — the username is not hyperlinked, just like how the user IDs of deleted users are listed in other places like in the list of close voters of a question, etc.  If this really were a deleted user, then I would have expected their user ID to be shown, and not &quot;anon&quot;. So, I checked using  for data on the tag synonym. And sure enough, it shows that the deleted user with the ID 147263 created the synonym. To double-check, I looked up the  and came across a bunch of synonyms created by &quot;anon&quot;. Checking with , these were all created by the now deleted user with the ID 80. Similarly, in the  there are several created by &quot;anon&quot;, but  says that these were created by the now deleted user with the ID 54262.  Feature request: Show the user ID of the tag creator under the &quot;Creator&quot; column in the list of tag synonyms if the user is deleted, to be consistent with how posts and actions by deleted users are attributed everywhere else. I have a weird port forwarding problem. I tried to open my port 22 to the outside network. I was able to access it as long as I am not inside the LAN. I can access it from my office for example. But from within the LAN, I can access the port using the local ip, but I can't access the port using the external IP. It's as if the router is blocking the loopback. I've check all my router settings, turned off anything firewall/filtering related. Any ideas? Is there any way to check whether a file is locked without using a try/catch block?    Right now, the only way I know of is to just open the file and catch any System.IO.IOException. Why is CDC capture failing due to a missing dbo principal Let $k^p = k$, $K = k(x)$ and $F = k(u)$ for some $u \in K$. Show that $K/F$ is separable $\iff u \not\in K^p$. Let $K$ be the rational function field $k(x)$ over a perfect field $k$ of   characteristic $p &gt; 0$. Let $F = k(u)$ for some $u\in K$, and write   $u = f(x)/g(x)$ with $f$ and $g$ relatively prime. Show that $K/F$ is   a separable extension if and only if $u\notin K^p$.   There is already a post on this but it has not yet been answered :   The truth is that I am very confused with this problem, I would like someone please help me to understand what happens with this exercise and explain to me how it could be done by giving me a help or something. I already have an approach for the left-to-right implication, but I do not know very well how good it is. Could someone help me with the other implication please? Thank you very much. I tried writing $y=x^{\sin x}$, so $\ln y=\sin x\ln x$. I tried to rewrite the function as $\ln(x)/\csc x$ and apply l'Hopital to the last function, but it's a mess.   Is there a by hand way to do it? Expressions - is there an easy and "visual" way to combine them into another expression? Read only field not working in page layout I have custom object called candidate. I have created field name called first name which is read-only in the page layout. Once a record is created with first name field populated I am able to edit that field. Why I am able to edit (I mean getting pencil icon). Can anyone suggest me for this issue? How to report issues with the mobile SE application Detect if program is running with full administrator rights NFL overtime: after a field goal, clock runs out on second team's possession Under the NFL's current "modified sudden death" overtime rules, if the first team scores a field goal, the second team is entitled to one more possession.  What happens if the clock runs out during that possession?  Suppose the score is tied 20-20 at the end of the 4th quarter. Team A wins the overtime coin toss and receives the kickoff to begin overtime.  After a long slow drive, Team A scores a field goal to make the score 23-20.  Now they kick off to Team B.  Team B is not able to score, and the overtime period ends with Team B still in possession.  What happens?   is not very explicit on this point.  Article 4 (a) says:     There shall be a maximum of one 15-minute period, even if the second team has not had an opportunity to possess the ball or if its initial possession has not ended. If the score is tied at the end of the period, the game shall result in a tie.   I think this means that Team A wins, 23-20, but I am not completely sure.  Has this ever happened in a regular-season NFL game? Electron flow and electric potential In the physics tutorial topic on current electricity it defines the positive terminal as the high potential terminal and the negative as the low potential. When talking about positive test charges this analogy makes sense, the charge moves from the +ve to the -ve where it loses potential till it has to be "topped" up by the cell.   What confuses me when they begin talking electrons. Using this analogy would mean that the electrons move from the -ve to the +ve but this means it would work against the electric field so the potential energy increases till it reaches the +ve terminal.   My question is how does this analogy, if it does, change to accommodate electrons? Does the electric field reverse so the -ve terminal is the high potential and the +ve the low potential?