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Sequences

Sequence

Fourier Transforms and Wave Packets

This is a unit that introduces the Fourier transform and its properties and then applies the Fourier transform to free particle wave packets in non-relativistic quantum mechanics. The activities and homework are listed here. Appropriate text materials for mini-lectures can be found in the chapter Fourier Transforms and Wave Packets in the free online textbook The Geometry of Mathematical Methods.

Activities

Problem

5 min.

Dimensional Analysis of Kets
Students consider the dimensions of spin-state kets and position-basis kets.

Lecture

30 min.

Compare & Contrast Kets & Wavefunctions
In this lecture, the instructor guides a discussion about translating between bra-ket notation and wavefunction notation for quantum systems.

Small Group Activity

60 min.

Quantum Calculations on the Hydrogen Atom
  • Eigenvalues and eigenstates
  • Measurements of energy and angular momentum for hydrogen atom
  • Quantum probabilities
  • Superposition of states
  • New degeneracies

Small Group Activity

30 min.

Representations for Finding Components
In this small group activity, students draw components of a vector in Cartesian and polar bases. Students then write the components of the vector in these bases as both dot products with unit vectors and as bra/kets with basis bras.