| 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 TDSWE 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. |
