Symbolic Quantum Operators for Dirac Notation in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg87109] Symbolic Quantum Operators for Dirac Notation in Mathematica*From*: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>*Date*: Tue, 1 Apr 2008 03:20:55 -0500 (EST)

Dear group About Quantum for Mathematica ( http://homepage.cem.itesm.mx/lgomez/quantum/index.htm ) Now you can define Symbolic Quantum Operators for Dirac Notation in Mathematica, please see this link: http://homepage.cem.itesm.mx/lgomez/quantum/defope/defope.html Before this improvement operators could be defined only through the explicit Dirac representation of their =93matrix elements=94 ket-on-bra. Now operators can be defined trough their operation on a ket. For example, rising (creation) and lowering (annihilation) operators of the harmonic oscillator are easily defined and used at the end of the document in this link http://homepage.cem.itesm.mx/lgomez/quantum/defope/defope.html Now the Quantum Random Walk is solved in the documentation by three different methods, which have different advantages and disadvantages. The last of these three methods uses the new feature of definition of symbolic quantum operators: FIRST: Q. Random Walker: Dirac Notation Approach: beautiful but slow: http://homepage.cem.itesm.mx/lgomez/quantum/qrwnaive/qrwnaive.html SECOND: Q. Random Waker: Mathematica Syntax Approach: Fastest but too specialized: http://homepage.cem.itesm.mx/lgomez/quantum/qrwefficient/qrwefficient.html THIRD: Q. Random Walker: Defining-operators approach: beautiful enough and fast enough, a good compromise: http://homepage.cem.itesm.mx/lgomez/quantum/qrwbest/qrwbest.html A colleague, Rub=E9n Dario, is already implementing new exciting Quantum Mechanics calculations (molecular collisions) using these new features. To have the new features, you must download the new Quantum.zip http://homepage.cem.itesm.mx/lgomez/quantum/Quantum.zip and install this new version according to the instructions in http://homepage.cem.itesm.mx/lgomez/quantum/installation/installation.html Enjoy it! Jose Luis Gomez-Munoz http://homepage.cem.itesm.mx/lgomez/