| Animation Speed {Δt} |
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Parameters
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Potential Steps The first few demos show how the transmission and wavefunctions are affected by potential boundaries. Use the spectral palette to set up a single energy eigenstate or a mixture of two or more eigenstates. If you don't create at least one energy state the program will use the current value of energy. (You can adjust this in the VaryIt panel.) Note that the boundary conditions for all wave functions are set at the IC point x = x(IC). The amplitudes ( R(0) and L(0) ) and phases (phiR and phiL) of right and left moving waves at that point determine the wavefunction at each energy. These values are adjusted using the animation VaryIt control which comes up before each demo or the Wave Animation Parameter panel accessed by the fourth button above. |
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Periodic Potential Barriers
These demos show how the transmission amplitude and wavefunction are affected by periodic sequence of n=1,2,.. or 5 potential barriers. To modify each one use the VaryIt panel to reset the x-interval ( a and b ) occupied by each hill or valley and their heights ( PE(a) and PE(b) ). Two types (PE Type = 1 or 2 ) correspond to square or sine hills, respectively. Note again that these values are adjusted using the animation VaryIt control which comes up before each animation or the Wave Animation Parameter panel accessed by the fourth button above. |
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Periodic Potential Wells Negative PE values give potential wells that have bound states as well as resonances. Use the zoom feature of the spectral palette to set energy values precisely on a bound state energy and a reasonable approximation of the eigenfunction should appear in the animation. |
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Kronig Penney Band Structure The band boundaries for Kronig-Penney potentials are computed. Select one of the square hump demos first and then adjust the lattice parameters a and b while running this demo. |
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Energy dependence of Wavefunctions The change in the wavefunction as the energy E or potential energy PE varies is shown by animation here. Select one of the square hump or well animations above first. Then select one of the animation buttons at the right. The range of variation is controlled by the Emin and Emax settings in the VaryIt panel. You can also reset the values of x=a and x=b as well as the potential energy values PE(a) or PE(b), whichever is not being varied. To get higher resolution choose as many frames as time and memory will allow, or make the energy range smaller. |
Animate wavefunction |
| Ψ = 0 |
| Ψ = 1 |
| Ψ = i |
| Ψ = -1 |
| Ψ = -i |
| 1 |
| 2 |
| 3 |