How does the photon absorption takes place in a hydrogen?  The classical mechanics shows the absorption of photonic energy resulting in the excitation of atom. Intuitively, a photon with frequency higher than that required for excitation of electron brings about the excitation process. But something restricts the excitation of electrons by photons of higher energy.   Why the match of energy of electron and the photon is an essential condition for excitation.  @Urgje said,     The probability of atomic excitation by photon absorption is given in terms of the "cross- section" for single photon absorption. This quantity shows a sharp peak if the photon energy and the atomic energy level difference match (the coupling between the atom and electromagnetic field causes the atomic states to broaden, the natural line width). Thus excitation by photons of higher energy is possible but its probability is very small.   What is meant by the cross section for single photon adsorption? Is there a electron excitation probability vs. Frequency of the photon plot?  What are the direct factors that affects there probability of the electron excitation?
This might be a stupid question, but nonetheless, it has been bothering me.  If you take a photon, make it go through some atoms in a solid, liquid or whatever, then you have the chance of this photon being absorbed by an electron, and thereby exciting the electron. This requires the photon to have enough energy to actually excite the electron to another energy level.  My question is then: How does the photon know if it has enough energy or not? Do they interact very quickly to determine if it's okay or not, or is it just something it "knows?"
Compound literals in MSVC In bash, read after a pipe is not setting values Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$. Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$. Is the converse true? I.e., if $g \circ f$ is invertible, does it follow that $f$ and $g$ are both invertible?  I know that if $f$ and $g$ are invertible, then they are both injective and surjective. Therefore, I assume from this that I have to show $g \circ f$ is injective and surjective as well, thus proving it is invertible. However, I don't know how to show $g \circ f$ is bijective based only on the information I have. Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$ Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$. Further Show that $v_0$ is the solution of some differential equation with appropriate boundary conditions. Compute $v_0$ explicitly.   Let $f: H^1(0,1) \to \mathbb{R}$ be defined by $f(u)=u(0)$. Then I showed that $f$ is linear and continuous. Hence there exists $v_0 \in H^1(0,1)$ such that $u(0)=\int_{0}^1u'v_0'+\int_{0}^1uv_0$  The differential equation is given by $f=-u''+u$ with the conditions $u'(0)=u'(1)=0$.   How do I compute $v_0$ explicitly?? Wave states with great confidence that Incursio is weaker than Grand Chariot, because Incursio was a prototype for Grand Chariot, etc.  The early clashes between Wave and Tatsumi can lead the viewer to such conclusion, but Incursio's has the ability to evolve (from the beast it was made of), while Grand Chariot doesn't.  If you watched to the finale, we can see that      Tatsumi causes Incursio to evolve so much during the fight against Shikoutazer that it even gains the ability to fly. While it is enough to defeat the emperor, unfortunately not enough to save Tatsumi's life.   Considering this, I don't think that Incursio was the weaker one. Is it so? How to escape @ characters in Subversion managed file names? ffmpeg is not even cutting this and other mp4s to the nearest second I'm trying to recall a story I read in the 1960s or 1970s, but which I suspect was older than that.  It was about a quasi-immortal family in the twentieth century who lived in a rural area and kept a low profile. It was a stand-alone story and only the family, and perhaps distant relatives, had unusual powers. I don't think they were aliens, just some offshoot of humanity.   They were of varying ages, ranging from relatively young to thousands of years old. They had lived in Europe before immigrating to the American colonies. Each person had a distinctive set of psi powers, ranging from the grandpa, pa, ma and son. I believe the youngest, just called Baby, was the most powerful and least human looking, and lived in the attic. He slept most of the time.  Nothing remains in my memory of the plot.  As I recall, the story had a Theodore Sturgeon feeling to it, with a humorous, ironic touch, but it probably wasn't his. I haven't been able to identify it from looking at a list of his works.  I probably read it in an anthology, but I might have seen it in an old magazine. I'm just not sure.  If anyone can help me identify it, I'd be grateful. Then I can scratch that mental itch. Is there a way to set app-specific volume? $\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists? I'm moving all files to a new computer, via an external hard drive. I am certain that broken links will be a concern. What can I do to fix this? Is there a 'Best Practices' kind of way to prevent this problem beforehand? I have many hundreds of .blend files, and of course, I fear losing them. Problem printing LaTeX from lua in lualatex I am having difficulty printing LaTeX from a lua function in a LaTeX document processed with lualatex (version 0.70.2). I have a sample that works (if I remove all newlines from the code) and a case that fails. I don't know why these get different results. Here is the sample that fails:  \documentclass{report} \usepackage{luacode} \begin{document}  \begin{luacode*} tex.sprint([[ \begin{tabular}{ | l | l | p{4.in} | }  \hline  {\bf File} &amp; {\bf Cards} &amp; {\bf Summary} \\ \hline  \end{tabular} ]]) \end{luacode*}   \end{document}   I get an error saying:  ! Misplaced \noalign. \hline -&gt;\noalign               {\ifnum 0=`}\fi \hrule \@height \arrayrulewidth \futurelet... l.22 \end{luacode*}   When I put all of the LaTeX code printed from lua on one line the code works fine:  \documentclass{report} \usepackage{luacode} \begin{document}  \begin{luacode*} tex.sprint([[ \begin{tabular}{ | l | l | p{4.in} | } \hline {\bf File} &amp;{\bf Cards} &amp; {\bf Summary} \\ \hline \end{tabular} ]]) \end{luacode*}   \end{document}   So I have a few question.  First, why does the first example shown above fail? It seems like something I am not aware of is being inserted into the generated LaTeX.  Also is there a way for me to see the actual LaTeX that is generated and processed so that I can debug issues like this better?  Is there a way to tell the lualatex to log the actual LaTeX it tries to process?  Any other suggestions for how to debug a problem like this? Given a DateTime object, how do I get an ISO 8601 date in string format? How to leave body of question empty? Update to Windows 10: What is going to happen to my data and apps? I have Windows 8.1 Update, if I update to Windows 10 when it becomes available what is going to happen to my data and apps?  Of course I have to do a backup, but I wonder if the data will be overwritten or not. Where can I rent a decent mountain bike in Zürich? I am going for a 4 day trip in Zürich and I would like to bike quite a lot. Though biking is quite advertised, I failed to find a decent bike rental shop in the city. Would highly appreciate some tips! Convert Latex to MathJax-HTML Is there any tool that can convert Latex documents to HTML documents, so that all math is presented with ?  (Obviously, it is fairly easy to hack together a quick Perl script that is able to do a crude conversion, but I am interested in a bit more robust solutions — at least it should get all cross-references right automatically.) Are all stormtroopers as poor soldiers as the ones in the movies? In the Star Wars films we consistently witness just how poor soldiers stormtroopers are. They show very sub-par marksmanship, crappy house searching tactics, and are easily fooled and defeated by Ewoks and Rebels.   That being said, I remember reading a character guide that defined stormtroopers as the very best of the best (best marksman, above average intelligence, etc.). So, in the realm of the Expanded Universe, does the mold that the movies set continue to hold true or are they just the exceptions to the rule? How to simplify the summation kk! without using induction? $$\sum_{k=1}^nk(k!)$$  I know the answer is (n+1)!-1..I can solve this question using principle of mathematical induction...but I would like to know if there is any other alternative approach If $f \colon [a,b] \rightarrow \mathbb{R}$, then show that there exists $c \in [a,b]$ such that $\int_a^c f = \int_c^b f$ If $f \colon [a,b]\rightarrow \mathbb{R}$, then show that there exists $c \in [a,b]$ such that $c \in [a,b]$ such that $\int_a^c f = \int_c^b f$.  I think that I have to proceed with the Mean Value Theorem of Integrals...