This applet depicts the quantum mechanical solutions to the two-dimensional particle in the box problem. Click on the "Lx+" to increase the length of the box in the x direction, and "Lx-" to decrease the length in the x direction. Similarly click on the "Ly+" or "Ly-" buttons to increase or decrease the length in the y direction, respectively.
Click on "nx+" to increase the x quantum number of solution, "nx-" to decrease. n=1 is the smallest legitimate quantum number for this problem, though the applet allows n to decrease to 0. When n=0, Ψ is identically zero everywhere, and Ψ Ψ*=0, so that the particle is nowhere in the box, which contradicts the premise that there actually is one particle in the box.
Click on the Ψ button to show the wavefunction, and on the Ψ2 button to show the probability density Ψ*Ψ. Notice that the button toggles between the two choices.
The values of the wavefunction are displayed in false color: blues indicate positive values (with black being the largest), reds indicate negative values (light gray being the smallest - most negative - values), and whites indicates a value of 0. Recall that when the wavefunction is 0, the probability density there is also zero, and we have a so-called node.
Allow sufficient time after clicking on a button for the changes to take effect, particularly if the box is large.
© 2004-2011 by Lawrence T. Sein. All rights reserved.
Send questions to: lseinjr@hotmail.com