Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Creation annihilation operators - expanding brackets

  1. Sep 10, 2012 #1

    yaj

    User Avatar

    I would like to normal order the following product of creation-annihilation operators, set up in Maple 16 as follows. The problem is, Maple won't perform "expand" (lowercase e) on the last step below (evaluating sigma3(x) :=[op1+op2]*[op3+op4]*[op5+op6] ); , which makes setting up the entire previous operator groups useless. Appreciate any help.
    Thanks
    yaj

    > with(Physics);
    > Setup(mathematicalnotation = true);
    print(`output redirected...`); # input placeholder
    [mathematicalnotation = true]
    > am1 := Annihilation(p, 1, notation = explicit);
    print(`output redirected...`); # input placeholder
    am1 := a-[p[1]]
    > ap1 := Creation(p, 1, notation = explicit);
    print(`output redirected...`); # input placeholder
    ap1 := a+[p[1]]
    > op1 := am1*exp(-i*p[1]*x);
    print(`output redirected...`); # input placeholder
    op1 := a-[p[1]] exp(-i p[1] x)
    > op2 := ap1*exp(i*p[1]*x);
    print(`output redirected...`); # input placeholder
    op2 := a+[p[1]] exp(i p[1] x)
    > am2 := Annihilation(p, 2, notation = explicit);
    print(`output redirected...`); # input placeholder
    am2 := a-[p[2]]
    > ap2 := Creation(p, 2, notation = explicit);
    print(`output redirected...`); # input placeholder
    ap2 := a+[p[2]]
    > op3 := am2*exp(-i*p[2]*x);
    print(`output redirected...`); # input placeholder
    op3 := a-[p[2]] exp(-i p[2] x)
    > op4 := ap2*exp(i*p[2]*x);
    print(`output redirected...`); # input placeholder
    op4 := a+[p[2]] exp(i p[2] x)
    > am3 := Annihilation(p, 3, notation = explicit);
    print(`output redirected...`); # input placeholder
    am3 := a-[p[3]]
    > ap3 := Creation(p, 3, notation = explicit);
    print(`output redirected...`); # input placeholder
    ap3 := a+[p[3]]
    > op5 := am3*exp(-i*p[3]*x);
    print(`output redirected...`); # input placeholder
    op5 := a-[p[3]] exp(-i p[3] x)
    > op6 := ap3*exp(i*p[3]*x);
    print(`output redirected...`); # input placeholder
    op6 := a+[p[3]] exp(i p[3] x)

    > sigma3(x) :=[op1+op2]*[op3+op4]*[op5+op6];
    print(`output redirected...`); # input placeholder
    sigma3 := Physics:-*(

    [a-[p[1]] exp(-i p[1] x) + a+[p[1]] exp(i p[1] x)],

    [a-[p[2]] exp(-i p[2] x) + a+[p[2]] exp(i p[2] x)],

    [a-[p[3]] exp(-i p[3] x) + a+[p[3]] exp(i p[3] x)])
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Creation annihilation operators - expanding brackets
  1. Energy in annihilation (Replies: 10)

Loading...