This is a simulation of the wave functions of a free particle with momentum states indexed by k and weighted by coefficients Ck where k is any integer, positive or negative. To alter the contributing states and their corresponding weights, click the input boxes on the left side of the simulation and change k to any positive or negative integer value, and Ck to any real number (note that Ck can theoretically be a complex number, but this simulation was not designed to handle complex values for Ck). The sum of all coefficients (\( \sum \) Ck) must not be zero. You can observe time evolution of the wave function by clicking "start/stop", and can reset the time value to zero at any time by clicking "reset t = 0". During time evolution of the wave function, you can click "measure P" to collapse the wave function to a specific momentum state, with probabilities proportional to squares of the states' Ck values. The “populate” button and slide allow you to quickly populate the inputs section with between 20 and 200 input boxes with Ck values of 1 to examine the contributing waves and overall wave function of a particle with many contributing momentum states. Press "reset defaults" at any point to reset the simulation to its default state.
This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Adam Holewinski and Neil Hendren under the direction of Professor John L. Falconer. This simulation was prepared with financial support from the National Science Foundation. Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.
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