Exactly Solvable Systems
PHYS 410 · Module 3
This module develops intuition through quantum systems that can be solved analytically. Students study the infinite and finite square wells, the harmonic oscillator, and tunneling through potential barriers.
Lessons in this module
The infinite square well
The infinite square well is the simplest model of a bound quantum particle. This lesson derives standing-wave eigenstates, quantized energies, and zero-point energy.
The finite square well
The finite square well is more realistic than the infinite well because the walls have finite height. This lesson explains bound states, exponential tails, and energy quantization by matching conditions.
The quantum harmonic oscillator
The quantum harmonic oscillator models vibrations near stable equilibrium. This lesson introduces quantized equally spaced energies, zero-point energy, ladder operators, and wavefunction structure.
Quantum tunneling
Quantum tunneling allows particles to pass through barriers that would be classically forbidden. This lesson explains evanescent waves, transmission probability, and major applications.
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