Continuation of the Application Quantum Algebra in Diracian Bra-Ket-Notation 

The application being published here continues the work of Cesar Guerra G. from 2004.

The following progress could be accomplished:

  • Support of current Mathematica versions
  • Certain functionality like Notations and Input Aliases has been moved into modules
  • The Input Aliases have been extended to Operators with indices
  • A new constant type was introduced (Complex Constant), which is used to simplify quantum expressions.
  • Bug fixing
  • New functionality allows for a stricter test of quantum expressions
  • Comprehensive Unit Tests
  • Documentation which can be integrated into Mathematicas documentation

About the Generation of the Application Quantum Algebra

When searching for a Mathematica application, being able to work with Quantum objects, I have found the equally named work of Cesar Guerra, that can be characterized as follows: (can be found in the Wolfram Library Archive)

  1. Supported Mathematica version: 4.1/4.2
  2. Author of the application: Cesar Guerra G.
  3. This application is no longer compatible with recent Mathematica versions
  4. This work has not been developed further since its publication

For this reason I try to develop Quantum Algebra with the following features:

  1. Support of recent Mathematica versions
  2. Usage of the current Notation Package
  3. Bugfixes, where bugs could be recognized
  4. Development, where I was able to do that

Structure of the Application 

The application consists of the following modules:


Module Content
Analyze.m Checks expressions for their type, for example Operator
Options.m Implements a few options for the whole application
QuantumAlgebra.m Contains the real non-commutative Quantum Algebra
QuantumNotation.m Supports the Dirac Bra-Ket-Notation and Input-Aliases

Provides styles for the graphical representation of the notation


Further this application contains a documentation, the work on which will be continued and unit tests for an intentionally complete test of the functionality.

Installation and Download

Quantum Algebra can run on Mathematica 10.x and has version number 1.1.1. Earlier versions of Mathematica must be checked.

To install download the ZIP - File and extract the application into your personal Applications folder of Mathematica. The documentation will then be available after a new start of Mathematica in the Documentation Center under Add-ons and Packages.

Additionally you can display the Notebook Preview of one tutorial in the browser.

Remark: Exactly speaking the sub folder QuantumAlgebra in the ZIP file must be extracted in the Applications folder. The whole ZIP file can be used as Wolfram Workbench project.


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