Quantum Tunneling

STEP 1: Changing the Potential Barrier Parameters

Click the "Barrier Parameters" tab (displayed by default, when the program starts).  You can change the shape as well as the dimensions of the barrier. Select the Shape of the Potential Barrier: Select the shape of the barrier from 4 choices (Square, Triangular, Trapezoidal, or User Defined). If you select User Defined barrier, the cursor in the potential energy graph changes into a pencil cursor.  A region bounded by an orange line appears, whose dimensions depend upon the current value of the Width and Height parameters.  Using the mouse sketch an arbitrary potential energy diagram in this region.

Change the Width of the Potential Barrier: Use the "Width" tab inside the "Barrier Parameters" tab.  The default width is 2x10-10m.  The "Scale Factor" can be changed using the spin control in the tab and the multiplying factor changed using the slider.  The value of the barrier width is displayed just below the top edge of the tab.  Observe the width of the potential barrier change at the top of the screen.  The horizontal scale of the potential energy graph may change to accommodate the complete barrier.  In case of the triangular and trapezoidal potential barriers, the width is defined at the base of the potential barrier.

Change the Height of the Potential Barrier: Use the "Height" tab inside the "Barrier Parameters" tab.  The default height is 4.0eV.  The "Scale Factor" can be changed using the spin control in the tab and the multiplying factor changed using the slider.  The value of the barrier height is displayed just below the top edge of the tab.

Observe the height of the potential barrier change at the top of the screen.  The vertical scale of the potential energy graph may change to accommodate the complete barrier.  In case of a Trapezoidal barrier, you must specify both the "Left height" and "Right height" of the barrier, using the appropriate tabs.

Change the Right Level of the Potential Barrier: Uuse the "Right Level" tab inside the "Barrier Parameters" tab. The default height is 0.0eV.  The "Scale Factor" can be changed using the spin control in the tab and the multiplying factor changed using the slider.  The value of the potential energy to the right of the barrier is displayed just below the top edge of the tab.  Observe this energy in the potential energy graph..  The vertical scale of the graph may change to accommodate the complete barrier.

Create Double Barriers: To create two identical barriers whose "Width" and "Height" you have specified using the appropriate tabs, click the Double Barriers checkbox.  The barrier that you had created is duplicated, and two identical barriers appear  in the potential energy graph, that are separated by a certain distance.  An "Interbarrier Distance" tab appears.  Change the value of the distance between the two barriers using the slider and "Scale Factor" spin control.  The default value is 2x10-10m.  The value of the interbarrier distance appears just below the top edge of the tab.

STEP 2: Changing the Particle Parameters

Click the "Particle Parameters" tab.  You can select the type of particle and change its energy. Select the Particle: Select the Particle of from 4 choices (Electron, Proton, Pion, or User Defined).  If you select "User Defined" particle, you can change the "Mass" of the particle using the appropriate tab.

Change the Total Energy of the Particle: Use the "Energy" tab inside the "Particle Parameters" tab.  The default energy is 3.0eV.  The "Scale Factor" can be changed using the spin control in the tab and the multiplying factor changed using the slider.  The value of the particle energy is displayed just below the top edge of the tab.

Observe the total energy (blue horizontal) change in the potential energy graph at the top of the screen.  The vertical scale of the graph may change to accommodate the energy.  In case of the "User Defined" particle you could also specify the wavelength of the particle, using the "Wavelength" tab.  The value of wavelength that you choose overrides the values of mass and energy that you chose earlier.

STEP 3: Observing the Wave Function and Probability Density

Having set the "Potential Parameters" and "Particle Parameters" in Steps 1 and 2 respectively, observe the wave functions and probability density distributions.

Click the "Real", "Imaginary", or "Probability Density" tab just below the potential energy graph and then click the "Redraw Graphs" button if it is blinking.  Within a few moments the program displays the desired graph below.  While performing the calculations the percentage of calculations completed will be indicated at the top left corner of the wave function graph.

STEP 4: Writing Comments, Printing, Saving, or Quitting a File

Make comments about observations by clicking the "Comments" button.  A frame pops-up on the screen.  Type in the required comments. Print your work using File/Print from the pull-down menu.  Save a file, including the comments, using File/Save from the pull-down menu. Quit the program by either clicking the "Quit" button or using File/Quit from the pull-down menu.

STEP 5 (Advanced): Change Planck’s Constant

Simulate what would happen in a hypothetical universe, where Planck’s constant had a different value!!.  Would macroscopic objects such as humans and cars be more or less likely to tunnel through barriers such as walls?

Change Planck’s Constant using the "Planck’s Constant" tab.  The default energy is 6.63x10-34Js (the real value of Planck’s Constant).  The "Scale Factor" can be changed using the spin control in the tab and the multiplying factor changed using the slider.  You can return to the default value by clicking the "Set Default" button in the tab at any time.  The value of the Planck’s Constant is displayed just below the top edge of the tab.

STEP 6 (Advanced): Observe the Tunneling Probability vs. Energy Graph

Observe how the tunneling probability of the chosen particle varies with energy for the chosen potential barrier.  Click the "T vs. E" tab just below the potential energy graph, and click the "Redraw Graphs" button if it is blinking.  The program solves for the probability density at six equally spaced values of energy starting from 0eV to the barrier height.  From the probability density graph at each value of energy the program determines the tunneling probability, and then generates a graph of these tunneling probabilities vs. the energy.  The process takes a several moments, and the Tunneling Probability vs. Energy (T vs. E) graph is jagged because it is created from only six data points.  The graph appears in place of the wave function graph.