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Commutators on Maple

  1. Apr 18, 2010 #1

    I'm trying to evaluate some commutators on Maple 12 and so far I have defined the rule for [tex][x_i^\alpha,p_j^\beta]=i\hbar \delta_{ij}\delta^{\alpha,\beta}[/tex], where [tex]i[/tex] denotes a space coordinate and [tex]\alpha[/tex] represents a particle. The code that I used for that is

    Setup(quantumop = {p, x}, algebrarule = {%Commutator(x[i, alpha], p[j, beta]) = I* hbar* KroneckerDelta[i, j]* KroneckerDelta[alpha, beta]})

    I'm trying to code a similar rule for

    [tex][p_i^\alpha,f(x)]=-i\hbar \frac{\partial}{\partial x_i^\alpha}f(x)[/tex], and I tried

    Setup(quantumop = {f, p}, algebrarule = {%Commutator(p[i, alpha], f(x)) = -I*hbar* Diff(f(x), x[i, alpha])})

    but it doesn't work. Does anyone know how to implement this rule? By the way, how can I implement the Einstein summation convention on Maple?

    Thanks for your help.
  2. jcsd
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