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Results: mathematica

computer Computer Simulation

30 min.

Approximating Functions with Power Series

Taylor series power series approximation

Power Series Sequence (E&M)

Students use a prepared Mathematica notebook to plot \(\sin\theta\) simultaneously with several terms of a power series expansion to judge how well the approximation fits. Students can alter the worksheet to change the number of terms in the expansion and even to change the function that is being considered. Students should have already calculated the coefficients for a power series expansion in a previous activity, Calculating Coefficients for a Power Series.

computer Mathematica Activity

30 min.

Effective Potentials
Students use a pre-written Mathematica notebook or a Geogebra applet to explore how the shape of the effective potential function changes as the various parameters (angular momentum, force constant, reduced mass) are varied.

computer Mathematica Activity

30 min.

Visualization of Quantum Probabilities for a Particle Confined to a Ring

central forces quantum mechanics angular momentum probability density eigenstates time evolution superposition mathematica

Quantum Ring Sequence

Students see probability density for eigenstates and linear combinations of eigenstates for a particle on a ring. The three visual representations: standard position vs probability density plot, a ring with colormapping, and cylindrical plot with height and colormapping, are also animated to visualize time-evolution.

group Small Group Activity

30 min.

Using Technology to Visualize Potentials
Begin by prompting the students to brainstorm different ways to represent a three dimensional scalar field on a 2-D surface (like their paper or a whiteboard). The students use a pre-made Sage code or a Mathematica worksheet to visualize the electrostatic potential of several distributions of charges. The computer algebra systems demonstrates several different ways of plotting the potential.
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