In solving finite square well problem, we solve the TISE inside and outside the well, and we match the wave function at the boundary, by the continuity of wave function. Now this bugs me, since the wavefunction is only assume to be square-integrable, why we can use the continuity of wavefunction? Edit: There is no problem for this bound state solution to hold, but will we miss other non-continuous solutions?
Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't mention anything.
Exclusive lighting Is (or will be) there any sort of light linking in Cycles, or a method to get a light to affect only certain objects that doesn't involve compositing two or more different render layers? Sort of what 3Dstudio does with the Include/Exclude methods. A file manager with free icon placing option How do shock waves form in space? Today my aerodynamics professor mentioned that the equations we were learning for atmospheric shock waves can also be applied by astrophysicists to study black hole-related shock waves in space.  How is this possible? Isn't space too rarefied for shock waves? What is an example application? He mentioned something about the density limit before/after a relativistic shock approaching 6. This is part of a homework assignment for a real analysis course taught out of "Baby Rudin."  Just looking for a push in the right direction, not a full-blown solution.  We are to suppose that $f(x)f(y)=f(x+y)$ for all real x and y, and that f is continuous and not zero.  The first part of this question let me assume differentiability as well, and I was able to compose it with the natural log and take the derivative to prove that $f(x)=e^{cx}$ where c is a real constant.  I'm having a little more trouble only assuming continuity; I'm currently trying to prove that f is differentiable at zero, and hence all real numbers.  Is this an approach worth taking? How to terminate a script? Index with exercise numbers If $A=AB-BA$, is $A$ nilpotent? Statement: $[a, b] \cap \mathbb{Q}$ in $\mathbb{Q}$ is not compact. Thus the interior of all compact subsets of $\mathbb{Q}$ is $\emptyset$.   I am trying to understand the first sentence. I read that a closed subspace of a compact space is compact, so for example, consider the unit interval $[0, 1]$ which is a compact space. Take a closed subspace $[0, 1] \cap \mathbb{Q}$ of $[0, 1]$. This set is closed since it just consists of all the rational numbers in between $0$ and $1$, including $0$ and $1$. So it is a closed subspace of a compact space. But why isn't this compact? Closing jFrame after clicking JButton Reading a 5 Band resistor with Gold as a middle band? Can anyone read the resistor that the arrow is pointing to?  From what I know you can not have a gold band as a number and if I am reading it correctly it has a tolerance of 0 which does not seem right. Converting string arrays into Map Number of ways in which $5$ boys and $5$ girls are ordered in such a way that exactly $4$ girls stand consecutively in the queue Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which $5$ boys and $5$ girls in such a way that exactly $4$ girls stand consecutively in the queue. Then find $\frac{m}{n}$.    I could find $n$ correctly as $6!\times 5!$, but I am finding $m$ as $7!\times 4!\times \binom{5}{1}$, but the book says $m$ is $6!\times 4!\times 5\times \binom{5}{4}$. Where have I gone wrong? What is the proper logic to find $m$? I have a basic grammar question about the past tense. If I met a guy yesterday, which tense should I use about his name today?  For example,     "Yesterday I met a guy, his name is/was John." Subquery in SQL Server Compact Edition count() returns a different amount than a simple select How can I position my div at the bottom of its container? Given the following HTML:   &lt;div id="container"&gt;   &lt;!-- Other elements here --&gt;   &lt;div id="copyright"&gt;     Copyright Foo web designs   &lt;/div&gt; &lt;/div&gt;    I would like #copyright to stick to the bottom of #container. Can I achieve this without using absolute positioning? I've tried searching for this question but couldn't find it on stackexchange. This is a common type of interview question; I ran into it doing brain teasers on a probability puzzles app, and if you fine people agree with my logic, I will inform the app developer that his/her answers are incorrect.   The problem is essentially this:  You are sentenced to death for thievery. The King is magnanimous and decides to put your fate in the hands of chance. You are given $100$ white marbles and 100 black marbles, and $2$ urns. The king will choose an urn at random and pull out a single marble at random; if the marble is white, you live, if its black, you die. If you place the marbles in the best way possible, what is your probability of survival?  I started with the base case: $100$ white marbles in one urn, $100$ black marbles in the other. This comes down to a $50$-$50$ chance of survival. I then worked my way to deciding that placing $1$ white marble in one urn and $99$ white marbles + $100$ black marbles in the other urn would be the "best way possible", which yields the following:  $$P(\text{Survival}) = \frac{1}{2}(1+\frac{99}{199}) \approx .749$$  Selecting $1$ of $2$ urns at random gives $\frac{1}{2}$, the urn containing $1$ marble gives $1$, and the other that contains $99$ white marbles and $100$ black marbles gives $\frac{99}{199}$ because there are $99$ possible white marbles to select out of $199$ total marbles.  The app claims that the correct answer is $\frac{1}{2}(1+\frac{99}{200}) \approx .748$   I see where the $200$ comes from, but I do not think it is right to say that there are $200$ marbles in the other urn. Who is correct? How can I repair the Windows 8 EFI Bootloader? What rolls should players get to see? I'm a new DM and over the last few weeks I've been slowly learning the game and how it runs. My party consists of 5 PCs.   One thing I have been wondering after our last two sessions is: What rolls should all the players see and which rolls shouldn't they see?  Is there a comprehensive list of what rolls are public and which go behind the DM screen, or is it more down to house rules or personal preference? PHPExcel Sumif and Skip