What does having an imaginary part of potential imply? In DJ Griffiths' ''Introduction to Quantum Mechanics&quot; to describe an unstable particle that spontaneously disintegrates he assumed an imaginary part in the potential. What does that signify? What is meant by an imaginary potential? I have added the image of the problem.
Quantum mechanics - how can the energy be complex? In section 134 of Vol. 3 (Quantum Mechanics), Landau and Lifshitz make the energy complex in order to describe a particle that can decay:  $$ E = E_0 - \frac{1}{2}i \Gamma. $$  The propagator $U(t) = \exp(-i H t)$ then makes the wavefunction die exponentially with time.  But also, $H$ is non-Hermitian.  My question: Do we have to modify the basic postulates of quantum mechanics (as described by Shankar, say, or the earlier sections of Landau &amp; Lifshitz) to describe unstable particles?
Does getting disconnected from an SSH session kill your programs? What are "first class" objects? When are objects or something else said to be "first class" in a given programming language, and why? In what do they differ from languages where they are not?  EDIT. When one says "everything is an object" (like in Python), does he indeed mean that "everything is first-class"? If I was... If I were...   When is it correct to use "If I was" vs. "If I were" in standard English? How do I properly use the "Not an Answer" flag? What is the "Not an Answer" flag and what is its purpose? When should I use this flag? When should I not use this flag? But I'm still not sure if I'm using the flag correctly... An answer is "Not an Answer", but the flag was declined or disputed!   See also: Transparent text cut out of background Is there word for this, other than know-it-all? Just wondering, if there's a word for:  One who makes it appear as if they're an expert on a subject while there are also signals (subtly or blatantly noticeable) that this person doesn't know very much on the subject or at least as much as they're acting like they do on the subject; pretending to have much knowledge on a subject matter.  I found pedantic but I don't suppose it's the right word. There is already a similar post, that has an answer to my question, but it is quite short and I don't get it... So I am trying to show that  \begin{align} \{e_K |~ K \subset G~ conjugacy~ class \} \end{align} is a basis for $Z(\mathbb{Z}[G])$. Serre even writes "one immediately checks that the $e_K$ form a basis", but even reading the other post  I don't see that...  My approach to this is:  Be $x \in Z(\mathbb{Z}[G])$, which is equivalent to: $x = gxg^{-1}$ for all $g \in G$. Writing  $x = \sum\limits_{h \in G} \lambda_h h$, we get $x = \sum\limits_{h \in G} \lambda_h ghg^{-1}$. I don't really know how to go on at this point. I mean, I know that when $a,b \in K$ (same conjugacy class) you get $\sum\limits_{s \in K} \mu_s s = \mu\sum\limits_{s \in K} s$, since \begin{align} a = hbh^{-1} \Rightarrow \mu_a = \mu_b ~\forall a,b\in K \end{align} So all elements in the same conjugacy class have the same scalar.  But from here I don't really know how I can generate the $x = \sum\limits_{h \in G} \lambda_h ghg^{-1}$ with the $e_K$ ...  I would be really thankful, if someone could give me quite a basic proof that even I understand... How to show $\omega^n$ is a volume form in a symplectic manifold $(M, \omega)$? I am trying to understand what mathematics is really built up of. I thought mathematical logic was the foundation of everything. But from reading a book in mathematical logic, they use "="(equals-sign), functions and relations.  Now is the "=" taken as undefined? I have seen it been defined in terms of the identity relation.  But in order to talk about functions and relations you need set theory.  However,  seems to be a part of mathematical logic.  Does this mean that (naive) set theory comes before sentential and predicate logic? Is (naive)set-theory at the absolute bottom, where we can define relations and functions and the eqality relation. And then comes sentential logic, and then predicate logic?  I am a little confused because when I took an introductory course, we had a little logic before set-theory. But now I see in another book on introduction to proofs that set-theory is in a chapter before logic. So what is at the bottom/start of mathematics, logic or set theory?, or is it circular at the bottom?  Can this be how it is at the bottom?  naive set-theory $\rightarrow$ sentential logic $\rightarrow $ predicate logic $\rightarrow$ axiomatic set-theory(ZFC) $\rightarrow$ mathematics  (But the problem with this explanation is that it seems that some naive-set theory proofs use logic...)  (The arrows are of course not "logical" arrows.)  simple explanation of the problem:  a book on logic uses at the start: functions, relations, sets, ordered pairs, "="  a book on set theory uses at the start: logical deductions like this: "$B \subseteq A$", means every element in B is in A, so if $C \subseteq B, B \subseteq A$, a proof can be "since every element in C is in B, and every element in B is in A, every element of C is in A: $C \subseteq A$". But this is first order logic? ($(c \rightarrow b \wedge b \rightarrow a)\rightarrow (c\rightarrow a)$).  Hence, both started from each other? I just discovered Matlab's factor()-function, and I randomly typed in 20081294819, and to my surprise it only had two factors (5099 and 3938281)! I had expected many more factors for such a big number and wondered how normal this was. The following is what I've done in my investigation so far.  In the first figure below, I have plotted the probability that some number below $10^k$ has $m$ indistinct prime factors.  The second figure shows the evolution of the probability of finding a number with $m$ indistinct prime factors as the numbers one is looking at grows, i.e. it is just another way to visualize the same data. I have left out all points of zero probability.  If one looks at the first part of the figure, it seems that the peak of the curve for some $k$ shifts toward higher $m$ as $k$ grows.   My first question is this: Does this behavior (i.e. the peak shifting toward higher $m$ as $k$ grows) continue indefinitely, or will the peak stabilize at some point? The latter seems unlikely but I can't be sure.  My second question is this: Approximately how fast does the peak-value $m_{peak}$ move as $k$ grows?  I briefly looked at the , but this involves distinct primes and I don't really know much number theory, so any help would be greatly appreciated! British Airways (BA) just changed our flight times, leaving us only 1h15mins for our layover in Heathrow. We arrive from Brussels in terminal 5 in Heathrow at 7:55 and our next flight leaves for Miami in Heathrow terminal 3 at 9:10.  This seems awfully short.   Does anyone know whether this is doable?   The flights are in November, so I'm still hoping that the flights will change back to the original flight times, which would give us an additional hour for the layover, but in case this does not happen, what are the chances that we will make the connecting flight in 1h15mins? I want to make a Launcher that will do privileged (requires root) commands, but I don't want to see the terminal or have to type my password into the terminal. So I found the command, gksudo that allows me to enter my password so that I can escalate my privilege level. Now I want to couple this, so that I can change the partition priority using this command cgpt add -i 6 -P 0 -S 0 /dev/sda (this command is privileged) and have it automatically reboot from this one launcher.  I setup a Luncher like this:  Name: ChromeOS  Description:  Command: gksudo gnome-terminal -e "cgpt add -i 6 -P 0 -S 0 /dev/sda;reboot"  Comment:  But it does not work. Any tips? If I wrote something in plperlu, when would that module be reloaded?  Every time the function ran?  The first time it ran?  Does the Perl DLL get unloaded if it hasn't been used in a while, and then after that it'd be another module reload? $$\int_{-\infty}^{\infty} \frac{\cos(αx)}{(x^2+1)(x^2+4)} \mathrm dx. $$  I am not sure how to solve this question. Can anyone help me to approach this problem. Thanks. What possessive forms are used for mutual 1st person ownership? I want to talk to someone about the house that my wife and I own.  Saying, for example, "My wife's and my house is awesome," sounds a bit funny to me.  What's the best way to express this?  Clarification  I'm asking specifically about the grammar of multiple nouns in possessive form.  I'm particularly curious if it's possible to do this with a first-person pronoun (me).  I am capable of rephrasing this in other ways - my question is not how to express the idea, but about this particular grammatical construction, if it is even legal. Restarting Mathematica causes an animation to fail to run Continuing example in Beamer Is there a program equivalent to lint for LaTeX? Is there a program equivalent to lint for LaTeX? (lint checks C code for syntax errors and possible mistakes.) Should I install the play disc or not? I hear both sides of the story. "Installing both discs will improve performance" or "Playing from the disc is best".  I've come across a few threads that say to install the play disc to a USB drive. Will the Xbox 360 even read from 2 different sources at once?   Someone please clear this up for me, for all of us.  Do I Install the second "play" disc or not, and why? Expected number of hamiltonian paths in a tournament The following theorem is from Alon&amp;Spencer's The probabilistic method, in the beginning of chapter 2:  Theorem 2.1.1: There is a tournament $T$ with $n$ vertices and at least $\frac{n!}{2^{n-1}}$ Hamiltonian paths.  Briefly the theorem is proved by looking at $X_\sigma$ the indicator random variable for a permutation $\sigma$ giving a Hamiltonian path, that is, satisfying $(\sigma(i),\sigma(i+1))\in T$ for $1\leq i \lt n$. Then   $\sum \mathbb{E}\left[X_\sigma\right] = \frac{n!}{2^{n-1}}$.  I don't understand where did this value ($\frac{n!}{2^{n-1}}$) came from! could someone explain it please?