Peer Review

Quantum Mechanics: 2D Circular Square Well Applet

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Overview:: This simulation shows wavefunctions in a hard walled, circular quantum well in 2D. Linear combinations of energy eigenstates can be created and viewed, or Gaussian wavepackets created and allowed to evolve in time. Quantities displayed include the quantum state in position and momentum, the angular momentum, the energy, and expectations and uncertainties for each of these properties.
Type of Material:: Java Simulation
Recommended Uses:: In-class or out-of-class illustrations of quantum properties.
Technical Requirements:: Java enabled browser.
Identify Major Learning Goals:: Visualization and conceptual understanding of quantum states in 2D and simple properties of angular momentum.
Target Student Population:: Upper level undergraduate or graduate quantum mechanics classes.
Prerequisite Knowledge or Skills:: Introduction to quantum states and quantum properties including angular momentum.

Rating:
Strengths:: This is an excellent illustration of quantum mechanical states and properties. The ability to create general linear combinations of states using the phasor interface allows the exploration of quantum superposition. The ability to display (and interact with the simulation using) energy levels, probability densities in position and momentum, expectation values, and uncertainties for position, momentum, and angular momentum makes this a a powerful tool.

The fundamental properties of quantum angular momentum, particularly simple to understand in 2D, can be observed. This can be used to explore the relation between phase and current.

The tool to measure energy or angular momentum is an interesting basic introduction to quantum measurements.
Concerns:: There is no description provided of the algorithms and physics used in this simulation to compute the time dependence of the states and the physical quantities measured.

When an energy level in the energy diagram is selected, only one of the two degenerate states corresponding to that energy is displayed. Although both states are highlighted on the phasor diagram, there is no indication that (or why) only one will be displayed.

Rating:
Strengths:: This simulation can be used to explore a number of physical properties of quantum states, including superposition, phase, separation of variables (in this case radial and angular) in solving for eigenstates, and measurement.
Concerns:: This applet is strictly qualitative so it can not be used directly for quantitative problems.

The instructor will need to create lesson plans or activities for the use of this applet in a class.

Rating:
Strengths:: This applet has an intuitive interface with most inputs controlled by the cursor.

A short, well written set of instructions on using the applets is provided.
Concerns:: Students may need some advice on using this applet to its full potential. There are many ways to view and interact with the states illustrated and they may not understand all the physics that is being shown.

Other Issues and Comments:: This is one java simulation in an extensive collection from the author. Topics include waves, acoustics, electricity and magnetism, quantum mechanics, and math problems. All of these applets have a similar interface and high quality presentations of physical systems.
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