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Re: Any quantum chemists / physicists?

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  • Subject: [mg30218] Re: Any quantum chemists / physicists?
  • From: adam_jurhs at (atjurhs)
  • Date: Thu, 2 Aug 2001 03:16:12 -0400 (EDT)
  • References: <9k5r6g$hc1$>
  • Sender: owner-wri-mathgroup at

Hello Gustavo,

I have two packages that make use of commutators.  The first one works
rather well but does not employ a paticulary pretty notation.  The
other doesn't work too well (it does have some functionality) but it
does have the standard Bra-Ket notation that we know and love.  This
notation package was actually produced by a fellow who worked for
Wolfram back in 1997.  Let me know if you'd like either set of codes,
and I'll try to dig them up.

Also, I wrote my Master thesis in Mathematica v3.0 on modeling quantum
dynamical systems via wavepackets and a lattice representation.  Below
is the abstract of my thesis.  If you are interested in that Mathematica code,
let me know and I'll send it along.

A computer based simulation method for finding general solutions to
the Time-Dependent Schrödinger Wave Equation (TDSWE) in multiple
dimensions is presented.  In particular, Mathematica is utilized to
analyze wavepacket propagation with a "Lattice Representation" for an
arbitrary, but specified, potential energy configuration.  The Lattice
Representation Model along with Fourier Transform principles enables
the Time-Development Operator to be computed across arbitrarily
complicated potential terms in the T.D.S.W.E. and provides for
arbitrarily exact numerical solutions.
This simulation technique has been applied to a diverse array of
quantum dynamic systems using a desktop personal computer. The
specific system presented for explanation of the model is that of an
electron wavepacket traveling down a Quantum Wire with an "Electron
Trap" potential.  This particular system was chosen because of its
increasing importance in applications to Nanotechnology and Quantum
Registries of quantum computers.  A second system presented, the
Harmonic Oscillator, is used for validation of the modeling technique.
The various "measurements" calculated by this model include, but are
not limited to, the system's Energy Expectation Values, Uncertainty
Values, Energy Spectrum, and an animated graphical depiction of the
wavepackets' time development.

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