This applet provides simulations of the time-dependent bound states in both position and momentum space of many different 1D quantum wells. Well types include square, harmonic, asymmetric, double, and well arrays, with the option in many cases to include an additional linear potential. The properties displayed in the simulation include energy eigenstates, wavefunctions in position and momentum space, current densities, expectation values and uncertainties. The time dependence of all properties is shown. The user has control over a wide range of properties of the states including the initial wavefunction.
Type of Material:
Java applet
Recommended Uses:
In-class demonstrations and hands-on conceptual exercises.
Technical Requirements:
Java-enabled browser
Identify Major Learning Goals:
Conceptual understanding of quantum states and their physical properties, time dependence, and the impact of measurements.
Target Student Population:
Mostly junior through first year graduate physics students, although this applet could be used for qualitative studies of modern physics in earlier classes.
Prerequisite Knowledge or Skills:
This depends on the use of the material. An introduction to quantum states, expectation values, and measurement would be useful.
Content Quality
Rating:
Strengths:
The comprehensiveness and flexibility of this applet makes this work outstanding. The material covered includes some of the most interesting and hard to visualize in advanced physics. The available potential well options cover both standard examples and several less well studied. Essentially all physical parameters of the system, such as well width and depth and mass and charge of the quantum particle, can be adjusted. The user has extensive control over both the states and information provided, including probabilities, amplitudes, phases, expectation values, and uncertainties.
One important strength of this applet is the ability for the user to make "measurements" of position, momentum, or energy and view the subsequent propagation of the state. This provides an illustration of the important issues of quantum measurements and their impact on states.
This applet has a place in almost any advanced quantum-mechanics course.
Concerns:
The fact that the states used in the simulation are limited to bound states is mentioned in the documentation, but there is no discussion of the impact this has on the results.
As pointed out in the directions, the "Coulomb" well is not strictly Coulombic. This fact should be pointed out to students.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This simulation is quite general and can show a wide variety of physical scenarios in one-dimensional quantum mechanics. Because of its highly graphical and interactive nature, this simulation be used for hands-on explorations of physics that is not otherwise easily understood.
Concerns:
There are no pedagogical materials or examples connected to this applet, so its use will require instructors to spend some time developing questions and lessons. In particular, the development of quantitative problems to go along with this simulation could be difficult.
This simulation is so comprehensive and broad that students may need help exploring the important aspects of the physical systems.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This applet includes many user interface elements that allow students to interact with the simulation. The drop-down menus and mouse-actions allow students and faculty to set up almost any configuration and explore its time evolution.
Directions are given that describe all the views and options and how to perform different operations on the states.
Concerns:
None noted.
Other Issues and Comments:
This simulation is highly recommended for quantum mechanics classes.
Creative Commons:
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