PHYSOP A Package for Operator Calculus in Quantum Theory

Short Description
(see M. Warns, Software Extensions of REDUCE for Operator Calculus in. Quantum Theory, Proc. of the IV inter. Conf. on Computer Algebra in …

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Content
PHYSOP
A Package for Operator Calculus in Quantum
Theory
User’s Manual
Version 1.5
January 1992
Mathias Warns
Physikalisches Institut der Universit¨at Bonn
Endenicher Allee 11-13
D-5300 BONN 1
Germany
Tel: (++49) 228 733724
Fax: (++49) 228 737869
e-mail: UNP008@DBNRHRZ1.bitnet
1 Introduction
The package PHYSOP has been designed to meet the requirements of theoretical
physicists looking for a computer algebra tool to perform complicated
calculations in quantum theory with expressions containing operators.
These operations consist mainly in the calculation of commutators between
operator expressions and in the evaluations of operator matrix elements in
some abstract space. Since the capabilities of the current REDUCE release
to deal with complex expressions containing noncommutative operators are
rather restricted, the first step was to enhance these possibilities in order to
achieve a better usability of REDUCE for these kind of calculations. This
has led to the development of a first package called NONCOM2 which is described
in section 2. For more complicated expressions involving both scalar
quantities and operators the need for an additional data type has emerged in
12 THE NONCOM2 PACKAGE 2
order to make a clear separation between the various objects present in the
calculation. The implementation of this new REDUCE data type is realized
by the PHYSOP (for PHYSical OPerator) package described in section 3.
2 The NONCOM2 Package
The package NONCOM2 redefines some standard REDUCE routines in order
to modify the way noncommutative operators are handled by the system.
In standard REDUCE declaring an operator to be noncommutative using
the NONCOM statement puts a global flag on the operator. This flag is checked
when the system has to decide whether or not two operators commute during
the manipulation of an expression.
The NONCOM2 package redefines the NONCOM statement in a way more
suitable for calculations in physics. Operators have now to be declared noncommutative
pairwise, i.e. coding:
NONCOM A,B;
declares the operators A and B to be noncommutative but allows them to
commute with any other (noncommutative or not) operator present in the
expression. In a similar way if one wants e.g. A(X) and A(Y) not…