The wavefunctions for a particle in a box are presented. A barrier in the middle of the box can be raised and widened so that the user can determine the effects on the energy levels of the available states and the distribution of probability amplitude for the wave function.
The purpose of this site is to provide a qualitative understanding of the effect of internal barrier widths and heights on energy levels for a particle in a modified box.
Target Student Population:
This is for advanced undergraduate Physical Chemistry students and graduate students in introductory quantum mechanics.
Prerequisite Knowledge or Skills:
Mathematical skills necessary to work with the wave equation are necessary for a student to be able to learn the background associated with this applet.
Type of Material:
It is a Java applet.
It could be used as a demonstration during a lecture presentation of the properties of a particle in abox.
Java applets must be permitted by the browser.
Evaluation and Observation
The applet is very interactive and gives a quick and clear idea of the effect of barriers of varying heights on the wavefunction and energy values of the particle. Since the equations are complicated, instructors will find this simulation an excellent aid to illustrates the underlying physical and chemical concepts that can be demonstrated by the quantum mechanics of a particle in a box. Students will appreciate seeing and playing with this excellent applet. Limits are set so that not much can go wrong. Some of the chemical and physical significance of the simulation is explained in the instruction page; more is left for the user to explore. The instruction even provides hints regarding the numerical methods used to calculate the wavefunctions. Potential applet authors may also find it interesting. Instructors can use this simulation without having to analyze the mathematical expressions.
The energy levels need to be enumerated. The box width needs to be specified. The rigor of the background textual information should be increased. The author should also consider upgrading the applet to include the effects of tunneling, albeit a slightly different application. Despite the nice explanation given in the instruction about wavefunctions, waves, standing waves and tunneling, the user has to know the quantum mechanics of a particle in a box to appreciate the underlying elegance and significance. The applet actually simulates a particle in a one-dimensional box with an internal barrier. The waves are more similar to standing waves of a string with fixed ends than to two-dimensional water waves or three dimensional sound waves.
Potential Effectiveness as a Teaching Tool
The ability to alter the height AND the width of the barrier is a major plus for this animation. Its use saves a lot of time for the instructors. Students will appreciate the visual display of changes of wavefunction and energy level, and thus increase their comprehension. Minute change of the barrier causes correspondent changes in the energy levels and wavefunctions. Thus, the simulation is very effective.
It would be useful to have the ability to plot probability density in addition to probability amplitude. A symbolic value for the energies of the levels should also be presented and axes need to be labelled and scaled to appropriate units. Students also might get the mistaken impression that these calculations are very easy so the instructor may have to explain what is really involved.
Ease of Use for Both Students and Faculty
This is an extremely fast loading and highly interactive applet.It uses graphics to show plots of the wave functions and energy levels of the quantum mechanical model of a particle in a one-dimensional box with a rectangular barrier in the middle. The user can change both the width and height of a potential barrier in the potential well, and observe the changes in the wavefunctions and energy levels. Barrier height and width are easy to change by dragging with a mouse. Response to change is instantaneous and accurate. Excellent separate instruction and credit pages eliminate cluttering the simulation, yet they provide excellent background reading regarding for the simulation.
The barrier height and barrier width should be in different colors (suggestion only) to emphasize that both can be varied. Consider having the operative equations which describe the energy levels changing as the barriers change,
but placed beside the graph. Also the first-time user is forced to read the Instruction Page, because there are no instructions on the simulation page.