Quantum Bound States

Topics

• Quantum Particles
• Potential Wells
• Waves
• Probability Density

Description

Explore the properties of quantum "particles" bound in potential wells. See how the wave functions and probability densities that describe them evolve (or don't evolve) over time.

Sample Learning Goals

• Visualize wave functions, probability densities, and energy levels for bound states in various potentials.
• Describe how multiple representations used for wave functions relate to one another.
• Explain what is and is not time-dependent for an energy eigenstate and a superposition state.
• Predict how the curvature and amplitude of the wave function and the spacing of the energy levels depends on the shape of the potential and the mass of the particle.
• Gain an intuition for how band structure results in a lattice of many wells.
• Gain an intuition for how to go from the microscopic potential of a single atom to the macroscopic potential of a solid.