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

( http://homepage.cem.itesm.mx/lgomez/quantum/index.htm  )

Now you can define Symbolic Quantum Operators for Dirac Notation in
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

http://homepage.cem.itesm.mx/lgomez/quantum/defope/defope.html

Now the Quantum Random Walk is solved in the documentation by three
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.

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/

```

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