This Java applet provides a visual representation of the "Particle in a One-Dimensional Box" problem. In this problem a particle of mass **m** is constrained to move along a line of length **a**. At the ends of the line are large potential energy barriers that keep the particle within the "box." In the quantum-mechanical treatment of the problem the Schrödinger wave equation is used to calculate the allowed energies of the particle. Since the potential energy inside the "box" is zero, the Schrödinger wave equation takes the form (eq 1)

The term is a differential operator and h is

where n called the

The applet below illustrates some important properties of the quantum-mechanical treatment of particles.

Select the mass (1.0e-27 or 2.0e-27 g) of the particle from the menu labeled "

The "

Complete the following exercises and answer the questions. See the Tutorial for Experiment: Particle in a One-Dimensional Box for an example and help.

- Select 2.0e-27 g from the "
**Mass**" menu and pick 7 Å from the menu labeled "**Width of Box**." Click the "**Start**" button. - Can the particle have any energy from zero to infinity?
- What are the values of n and E
_{n}for the particle? - Does the speed (magnitude of the velocity) of the particle change with time?
- Does the energy of the particle change with time?
- Select 4434 Å from the pull-down menu labeled "
**Wavelength**" and illuminate the particle in exercise #1. - Did the energy of the particle change? If your answer is yes, what is the new energy of the particle?
- Is the speed of the particle different from the speed observed in the previous exercise? To return to the animation in exercise #1, click the "
**Stop**" button, set the "**Wavelength**" to 0, and click the "**Start**" button.*Return to the animation in this exercise by selecting 4434 Å from the "***Wavelength**" menu. - Is y
_{n}for the new energy E_{n}the same as y_{1}? If your answer is no, how do the wave functions differ? To revisit the plot of y_{1}versus x, click the "**Stop**" button, set the "**Wavelength**" to 0, and click the "**Start**" button.*Please return to the E*_{n}energy level by selecting 4434 Å from the "**Wavelength**" menu. - Does the energy of the particle change with time?
- Does the speed of the particle change with time?
- Select 6999 Å from the pull-down menu labeled "
**Wavelength**" and illuminate the particle in exercise #2. - Did the energy of the particle change? If your answer is yes, what is the new energy of the particle?
- Does the energy of the particle change with time?
- Does the speed of the particle change with time?
- Select 5068 Å from the pull-down menu labeled "
**Wavelength**" and illuminate the particle in exercise #3. - Did the energy of the particle change? If your answer is yes, what is the new energy E
_{n}of the particle and what is the value of the quantum number n? - Is y
_{n}for the new energy E_{n}the same as y_{n}for the energy E_{n}in exercise #2? If your answer is no, how do the wave functions differ? To revisit the plot of y_{n}in exercise #2, click the "**Stop**" button, set the "**Wavelength**" to 4434 Å, and click the "**Start**" button.*Return to the E*_{n}energy level in this exercise by selecting 5068 Å from the "**Wavelength**" menu. - Does the energy of the particle change with time?
- Does the speed of the particle change with time?
- In order for the particle to gain energy what must happen?

If you have preformed all of the exercises, answered all of the questions, and completed the report to be submitted for credit, then you may check the Answers to Particle in a One-Dimensional Box Questions

Dr. Nutt's CHE 115 Course |