Harmonic Oscillator

This simulation illustrates the wavefunctions and time evolution of the quantum harmonic oscillator.

  • The input table (upper left corner) can be edited to change the quantum number n and expansion coefficient Cn
  • Time evolution can be observed with the Start/Stop button, and a probabilistic collapse of the wavefunction can be seen with the “Measure E” button.
  • The mass of the particle m and force constant kf are adjustable with sliders
  • The integrated probability density can be computed over any position range with the lower input table and the Integrate button. The lower limit of integration is designated x1 and the upper limit is x2. The integrated probability appears under the box labeled, “integral”.
  • The plot on the right displays the energy of each quantum state (dashed lines). Only the energy states under the “n” column of the input table are displayed.
  • The plot on the right also displays the well potential (dotted blue line), the wave function Y(x,t) (solid black line), and the total energy of the particle (solid red line).
  • Real and imaginary components of the wave, as well as total system energy, are additionally shown on the bottom-left plot.
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This simulation was made at the University of Colorado Boulder, Department of Chemical and Biological Engineering.  Author(s): Sky Christana, Neil Hendren
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