Start SHO-. Superpotential: W = x-a / Potential: V- = (x-a)2-1
Start SHO+. Superpotential: W = x-a / Potential: V+ = (x-a)2+1
Start AnHO-. Superpotential: W = x2-a / Potential: V- = (x^2-a)2-2x
Start AnHO+. Superpotential: W = x2-a / Potential: V+ = (x^2-a)2+2x
Start Sin-. Superpotential: W = a*Sin(x) / Potential: V- = a*Cos(x)+a2*Sin2(x)
Start Sin+. Superpotential: W = a*Sin(x) / Potential: V+ = -a*Cos(x)+a2*Sin2(x)
From the superpotential, W, SUSY quantum potentials (V- and V+) and groundstate wavefunctions (- and +) are calculated. A plot of the potential and wavefunction is shown for both the (-) and (+) solutions as a function of the arbitrary parameter a. Note the lack of sensitivity to this parameter: SUSY remains good/bad (meaning the wavefunction is either normalizable or it is not) for a wide range of values[Dunne et.al.]. Also note that only one (good SUSY) or neither (bad SUSY) of the pair of potentials has a normalizable wavefunction in the first two pairings. However in the last pairing SUSY is good for both cases which is a property of periodic potentials.
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Page created by Dr. Mario Belloni with thanks to Dr. Gerald Dunne at the University of Connecticut for his suggestions regarding these Physlets.