Because of the frequent use of anticommutative and noncommutative variables, functions, vectors, tensors and matrices; specialized rules and operators; and extremely complex notation, algebraic computations in physics are a serious challenge for most mathematical software. While some specialized systems handle a small fraction of this domain, Maple is the only system that provides the ability to handle a wide range of physics computations as well as pencilandpaper style input and textbookquality display of results. In addition, the Physics package is an integral part of the entire Maple system, so using Maple for physics also gives you access to Maple’s full mathematical power, programming language, visualization routines, and document creation tools.
The chart below lists Maple’s capabilities in algebraic computations in physics. In every case, problems in that area can be expressed in Maple using the same notation as you would use when writing the problem on paper, and the results are displayed in the same way as they would be shown in a textbook.
A complete summary of the Physics Package and its commands is also available.
Updates to the Physics Package
Substantial improvements to the Physics Package are made continually!
See the new features added in:
Download the Latest Updates to the Maple Physics Package
The current version of Maple includes the latest official release of Physics, and improvements are ongoing. You can take advantage of this ongoing work by downloading the research version of Physics as it is updated with improvements, fixes, and the very latest new developments.
Vector Analysis 
Quantum state vector calculus (Dirac’s notation) 


Tensor Analysis (ndimensional Geometry, Special and General Relativity) 
Field Theories (Classical and Quantum) 


Product Operators 
Differentiation Operators 


Differential Equations Support 
Differential Geometry Support 


Dig deeper: Overview of the Physics Package and List of Commands
Some examples of computations in Physics
Dig Deeper: More examples from the Physics Package
Mechanics: Lagrangian for a pendulum
The Lagrangian is defined as
b) The steps are the same as in part a:
Electrodynamics: Magnetic field of a rotating charged disk
Problem
Solution