<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=utf-8"> <META content="MSHTML 6.00.6000.16788" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY style="WORD-WRAP: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space" bgColor=#ffffff> <DIV><FONT face="Courier New" size=2>Ok, I am sure you are sure are familiar with the mather (:.</FONT></DIV> <DIV><FONT face="Courier New" size=2>You did show a nice example of currying, no doubt about that.</FONT></DIV> <DIV><FONT face="Courier New" size=2>Jos</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B> <A title=gregory.woodhouse@gmail.com href="mailto:gregory.woodhouse@gmail.com">Gregory Woodhouse</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A title=jos.koot@telefonica.net href="mailto:jos.koot@telefonica.net">Jos Koot</A> </DIV> <DIV style="FONT: 10pt arial"><B>Cc:</B> <A title=plt-scheme@list.cs.brown.edu href="mailto:plt-scheme@list.cs.brown.edu">PLT List</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, January 02, 2009 4:48 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [plt-scheme] Currying and physics</DIV> <DIV><BR></DIV> <DIV>Yes, I did. I even called it P!</DIV> <DIV><BR></DIV><BR> <DIV> <DIV>On Jan 2, 2009, at 1:16 AM, Jos Koot wrote:</DIV><BR class=Apple-interchange-newline> <BLOCKQUOTE type="cite"><SPAN class=Apple-style-span style="WORD-SPACING: 0px; FONT: 12px Helvetica; TEXT-TRANSFORM: none; COLOR: rgb(0,0,0); TEXT-INDENT: 0px; WHITE-SPACE: normal; LETTER-SPACING: normal; BORDER-COLLAPSE: separate; orphans: 2; widows: 2; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0"> <DIV><FONT face="Courier New" size=2>You probably mean (linear) momentum. Position can be represented by an operator (function, functional) Ψ -> xΨ. The probability to find the particle at position x at time t is:</FONT></DIV> <DIV><FONT face="Courier New" size=2>integral over x of Ψ*(x,t) x Ψ(x,t) divided by</FONT></DIV> <DIV><FONT face="Courier New" size=2>the integral over x of Ψ*(x,t) Ψ(x,t)</FONT><FONT face="Courier New"><FONT size=2>,</FONT></FONT></DIV> <DIV><FONT face="Courier New"><FONT size=2>where Ψ*</FONT></FONT><FONT face="Courier New"><FONT size=2><SPAN class=Apple-converted-space> </SPAN>is the complex conjugate of Ψ.</FONT></FONT></DIV><FONT face="Courier New"><FONT size=2></FONT></FONT> <DIV><FONT face="Courier New" size=2>In this case momentum is represented by the function Ψ -> (iħ/2π)(δΨ/δx).</FONT></DIV> <DIV><FONT face="Courier New" size=2>You could have choosen Ψ(x)=1/(1+x^2) as a function with finite norm,</FONT></DIV> <DIV><FONT face="Courier New" size=2>or in three dimensions 1/(1+x^2+y^2+z^2)</FONT></DIV> <DIV><FONT face="Courier New" size=2>In practice wave functions are often represented by time independent vectors (called kets) in a Hilbert space.</FONT></DIV> <DIV><FONT face="Courier New" size=2>Which functions Ψ</FONT><FONT face="Courier New"><FONT size=2><SPAN class=Apple-converted-space> </SPAN>are to be included in this space is determined by the law of conservation of energy. In quantum mechanics this law says: HΨ=EΨ, where H is the so called Hamiltonian (an operator representing energy) and E a real number. The equation must be solved for both Ψ and E (and the solution usually consists of an infinite number of pairs Ψ and E) By using the symmetry properties of the system being studied, many parts of the integrals can be simplified to summations.</FONT></FONT></DIV><FONT face="Courier New"><FONT size=2></FONT></FONT> <DIV><FONT face="Courier New" size=2>Jos</FONT></DIV> <DIV><FONT face="Courier New"><FONT size=2><FONT face="Courier New" size=2></FONT></FONT></FONT> </DIV></SPAN></BLOCKQUOTE></DIV><BR></BLOCKQUOTE></BODY></HTML>