Start SHO. Superpotential:
W=x-a / Potential: (x-a)^{2}-1

Start AnHO.
Superpotential: W=x^{2}-a / Potential: (x^{2}-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.

See more physlets:

Back to SUSY physlets page:

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.