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Re: Any quantum chemists / physicists?
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.