Start SHO. Superpotential: W=x-a / Potential: (x-a)2-1
Start AnHO. Superpotential: W=x2-a / Potential: (x2-a)2-2x
Start TANH1. Superpotential: W=tanh(x)-a
Start TANH2. Superpotential: W=x-a tanh(x)
From the superpotential, W, a SUSY quantum potential (V-) and a groundstate wavefunction is calculated. A plot of all three is shown 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 and in the third case SUSY is only good when -1>a>1[Dunne et.al.]. The fourth case is an example of good SUSY, where for certain values of a, the system exhibits quantum mechanical tunneling as the potential gets a "hump" in the middle. Note: the cases where SUSY is good (the wavefunction is normalizable) occur where the superpotential has a different sign as x=> infinity and x=>-infinity.
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This page was written by Dr. Mario Belloni with thanks to Dr. Gerald Dunne at the University of Connecticut and Dr. Wolfgang Christian at Davidson for their suggestions regarding these Physlets.