<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><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="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -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></body></html>