“Particle in a Box”
Particle in a Box
Oct 26, 2005
- 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.
- Type of Material:
- It is a Java applet.<br />
- Recommended Uses:
- It could be used as a demonstration during a lecture presentation of the
properties of a particle in abox.
- Technical Requirements:
- Java applets must be permitted by the browser.
- Identify Major Learning Goals:
- 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
- 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.
- 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
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
- 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.
- 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.
- 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.
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,
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.
- Creative Commons: