Peer Review

1D Quantum Crystal Applet

Material Detail page

Reviewed:: Jan 26, 2007 by Physics

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Ratings

Overall Rating:

Content Quality:

Effectiveness:

Ease of Use:

Overview:: This applet provides simulations of the quantum mechanical states in a 1D periodic potential. A number of different potential well shapes are available, including square, coupled pairs, harmonic, coulombic, and sinusoidal. Users can also create their own periodic potential wells.
The simulation displays the states in the well and the energy vs. crystal momentum dispersion.
Type of Material:: Java applet
Recommended Uses:: In-class or out-of-class illustrations of quantum states in crystals.
Technical Requirements:: Java enabled browser.
Identify Major Learning Goals:: Help with the visualization of states in periodic potentials and electron properties in crystals.
Target Student Population:: Upper level undergraduate or graduate solid state or quantum class
Prerequisite Knowledge or Skills:: Familarity with quantum mechanics and some background in solid state physics

Content Quality

Rating:

Strengths:

This is a clear illustration of the quantum mechanics of periodic potentials. The number of different potentials allows the qualitative study of the impact of potential size and shape. Changes in well shape and periodicity can be used to explore the basic concepts of Bloch states.

The energy dispersion display is particularly useful for this applet. The standard ways to display Brillouin zones (reduced, repeated, extended) are available. This gives different views of changes in states throughout the zones.

Concerns:

The applet will display both the wavefunction and the Bloch function, but students might not see immediately the distinction, and in some views there is no difference.

This applet only allows periodic potentials, so that it can't be used to study "impurities". This capability is available in a different applet by the same author for a finite array of wells.

There is no indication of the algorithm and physics used in this simulation to compute the states and the time dependence.

There are links to reference material from the Wikipeadia for terms used in the instructions for the simulation. Instructors may wish to check these references before assigning the simulation to students.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

This applet can be used to explore a number of qualitative properties. These include:

Changes in potential depth and their impact on states and band gaps.
Changes in potential periodicity and the results of creating or removing symmetries.
Changes in states and crystal momentum as energy changes through a Brillouin zone.
Changes in states across energy gaps.

Concerns:

The applet is purely qualitative, so it can not be used directly for quantitative problem solving.

Lesson plans and activities for using this applet for learning will need to be developed by the instructor.

Ease of Use for Both Students and Faculty

Rating:
Strengths:: This applet has most displays of information controled by the cursor.
A short, well-written set of instructions on using the applet is available.
Concerns:: There are a large number of options available for this applet, so that students may need some direction as to the best parameters to explore.

Other Issues and Comments:: This is one applet in an extensive collection covering waves, acoustics, electricity and magnetism, quantum mechanics, and math concepts. All of these applets are quite similar in structure and high quality.
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