Quantum Mechanics with Mathematica

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Quantum Mechanics with MathematicaA tutorial for instructorsDaniel V. SchroederWeber State UniversityJuly 2019IntroductionFor more than 20 years I have used Mathematica as a computational and visualizationtool when I teach Quantum Mechanics both at the upper-division level and in asophomore-level modern physics course. My goal in this tutorial is to help otherinstructors do the find Mathematica useful (in fact, almost indispensable) in these courses forseveral reasons: It allows students to quickly and easily plot any function, directly from itsformula, often with only a single line of code. With only a little more effort students can produce multidimensional plots,animated plots, and plots of complex-valued functions that use color hue torepresent phase.

Special functions such as Hermite polynomials and spherical harmonics are built into Mathematica. Mathematica provides easy-to-use routines for numerical integration, solving ODEs, and diagonalizing matrices. Coding a PDE-solving algorithm is no harder in Mathematica than in any other language (although execution speed can sometimes be an issue).

  Polynomials, Hermite, Hermite polynomials