# CCL: Question Szabo/Ostlund Ex.1.14

• From: Jozsef Csontos <jcsontos.lists * gmail.com>
• Subject: CCL: Question Szabo/Ostlund Ex.1.14
• Date: Fri, 04 Nov 2011 11:27:18 +0100

 Dear Martin, Please compile the followings with latex, \documentclass[a4paper,10pt]{article} \usepackage{ucs} \usepackage[utf8x]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{fontenc} \usepackage{graphicx} \usepackage[dvips]{hyperref} \author{JCsontos} \title{1.14 Szabo-Ostlund} \date{11/04/11} \begin{document} Â\begin{align*} Â \int_{-\infty}^{\ \infty}{a(x) \cdot \delta(x)}\ dx & = Â \int_{-\infty}^{-\epsilon}{a(x) \cdot 0}\ dx + Â \int_{-\epsilon}^{\ \epsilon}{a(x) \cdot \delta_{\epsilon}(x)}\ dx + Â \int_{\ \epsilon}^{\ \infty}{a(x)\cdot 0}\ dx \\ Â & = \int_{-\epsilon}^{\ \epsilon}{a(x) \cdot \delta_{\epsilon}(x)}\ dx \\ Â & = \int_{-\epsilon}^{\ \epsilon}{a(x) \cdot \frac{1}{2\epsilon}}\ dx \\ Â & = \lim_{\epsilon \to 0} \frac{1}{2\epsilon} \int_{-\epsilon}^{\ \epsilon}{a(x)}\ dx\\ Â & = \lim_{\epsilon \to 0} \frac{1}{2\epsilon} Â {[\epsilon-(-\epsilon)]}{a(\xi)}, \ \xi \in (-\epsilon, \epsilon) Â ;\ \textbf{mean value theorem for integration} Â\end{align*} \begin{align*} \text{if $\epsilon \to 0$ then $\xi \to 0$ and } Â \lim_{\epsilon \to 0} \frac{1}{2\epsilon} Â {[\epsilon-(-\epsilon)]}{a(\xi)} & = Â \frac{2\epsilon}{2\epsilon}{a(0)} \end{align*} \end{document} Best, Jozsef On 11/03/2011 04:56 PM, Martin Hediger ma.hed-x-bluewin.ch wrote: Sent to CCL by: "Martin Hediger" [ma.hed^^bluewin.ch] Dear List I also posted this question to the google.gamess user group, but was encouraged to do so here. I'm new to the CCL and looking forward to interesting discussions. I was trying to solve ex. 1.14 from Szabo/Ostlund. If d(x) = \lim_{eps->\infinity} d_eps(x), where d_eps(x) = 1/(2eps) when -eps <= x <= eps and d_eps(x)=0 else, we are supposed to show that the value of a function a(0) = \int dx a(x) d(x) My Ansatz was to insert the definition into the integral, but then I'm not exactly seeing how to treat the limit function. How does one show this? Thank you for any suggestions. MartinE-mail to subscribers: CHEMISTRY++ccl.net or use: http://www.ccl.net/cgi-bin/ccl/send_ccl_message E-mail to administrators: CHEMISTRY-REQUEST++ccl.net or use http://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp://www.ccl.net/chemistry/sub_unsub.shtml Before posting, check wait time at: http://www.ccl.net Job: http://www.ccl.net/jobs Conferences: http://server.ccl.net/chemistry/announcements/conferences/ Search Messages: http://www.ccl.net/chemistry/searchccl/index.shtmlhttp://www.ccl.net/spammers.txt RTFI: http://www.ccl.net/chemistry/aboutccl/instructions/