# Question:ordered product of creation and annihilation operators - expand

## Question:ordered product of creation and annihilation operators - expand

Maple 16

Hello,

I am trying to find the product of three groups of creation and annihilation operators. After completing the input of the groups, Maple fails to give me the product of the operators (value of sigma^3) as shown below. What I need is for Maple to give me the ordered product of the three groups, but the "expand" command (lowercase 'e') fails to produce any output. Appreciate any help.

> 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)])

﻿