momentum_and_position_op.mac

/* Maxima code for working with the quantum angular momentum operators

   Barton Willis
   Professor of Mathematics
   University of Nebraska at Kearney

Copyright (c) Barton Willis, 2021
GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007
*/
/* Declare the reduced Planck constant to be constant. That makes ħ outative for 
   a linear operator. Also define it to be positive*/
declare(ħ,constant);
assume(ħ > 0);

/* The one-dimensional case */
Q_p(e) := not mapatom(e) and inpart(e,0) = 'Q;
P_p(e) := not mapatom(e) and inpart(e,0) = 'P;

put(Q,Q,'operator_adjoint);
put(P,P,'operator_adjoint);

declare([Q,P],linear);
declare([Q,P],operator);

put(P, lambda([q], -%i*ħ*diff(q,x)), 'formula);
put(Q, lambda([q], x*q), 'formula);

/* Implement the rule P Q --> Q P  - %i*ħ */
simp_P(e) :=
  if Q_p(e) then Q(P(first(e))) - %i*ħ*first(e)
  else simpfuncall('P,e);

simplifying('P, 'simp_P);