The curricular material uses the QMSuperpositionApp to show wave functions in color-as-phase representation (ħ = 2m = 1). In color-as-phase representation the amplitude of the wave function is depicted as the distance from the bottom to the top of the wave function at a given point and time. The phase is depicted as the color of the wave function with a map between phase angle and color. In quantum-mechanical time evolution, the phase evolves clockwise in the complex plane in time.
Time-dependent quantum-mechanical wave functions are inherently complex (having real and imaginary components) due to the time evolution governed by the Schrödinger equation, which in one-dimensional position space is
[−(ħ2/2m)∂2/∂x2 + V(x)] ψ(x,t) = iħ(∂/∂t) ψ(x,t) .
The standard way to visualize the wave functions that solve this equation is to either consider just the real part or consider the probability density, approaches that discard all phase information. We use color-as-phase representation of the wave function to display this information in a meaningful way.
There are two options in how to run these exercises:
| Run Locally | Run via Browser |
|---|---|
| Download the osp_qm_superposition.jar and osp_qm_worksheet1.pdf files. Double-click the “osp_qm_superposition.jar” file. When the jar file opens, select the “QM Worksheets” tab at the bottom of the Launcher window. Navigate to the "Energy Eigenstate Shape" folder where you will find the interactive curricular materials that go with these exercises. | To run via your web browser, simply select one of the links in the outline after the "Description" link. |
You may directly access (browse) the binary directory containing jar files. Note that the binary directory also contains code libraries (jar files) that are not designed to run as stand-alone applications.