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.