## Matrix Representation

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Dear Members,\n\nOn p. 30 of Sakurai\'s Modern Quantum Mechanics, why in (1.4.28),\n&lt;a"|B|a\'&gt; represents Matrix elements of B?\n\nCheers,\nAli\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Members,

On p. 30 of Sakurai's Modern Quantum Mechanics, why in (1.4.28),
<a"$|B|a'>$ represents Matrix elements of B?

Cheers,
Ali



On $2005-06-01,$ Ali wrote: > Dear Members, > > On p. 30 of Sakurai's Modern Quantum Mechanics, why in (1.4.28), >[/itex] represents Matrix elements of B? The short answer answer is: By definition. Longer answer. Let ${|1>, |2>, ...}$ be an orthonormal basis for the Hilbert space. B is a linear operator that maps the Hilbert space into itself. Let |a> be a vector and $|b> = H|a>$. Expand both vectors in the chosen basis: $|a> = a_1|1> + a_2|2> + ..., |b> = b_1|1> + b_2|2> + ...$ Relate the coefficients (by orthonormality): $b_i = = = sum_j a_j$. If you consider $b_i$ to be entries in a column vector, then this column vector is obtained by multiplication of a matrix with elements  with another column vector with entries $a_j$. That is why the numbers  are called matrix elements of the operator B. How are you doing with that supplementary book on linear algebra? Igor



"Ali" wrote in message news:1117598940.983572.265940@z14g20...egroups.com... > Dear Members, > > On p. 30 of Sakurai's Modern Quantum Mechanics, why in (1.4.28), > [/itex] represents Matrix elements of B? > > Cheers, > Ali > Use the facts that $= a'|a'>$ along with the definition of the commutator. John Lowry Flight Physics