[Date Index] [Thread Index] [Author Index]

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/