Personally I enjoy describing new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics, and multi-soliton solutions of the KdV equation are constructed. Approximation methods within the framework of supersymmetric quantum mechanics and in particular it has shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate inside a double well potential and for improving large $N$ expansion although i digress.
Personally I enjoy describing new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics, and multi-soliton solutions of the KdV equation are constructed. Approximation methods within the framework of supersymmetric quantum mechanics and in particular it has shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate inside a double well potential and for improving large $N$ expansion although i digress.
Just because you can make perfect higher dimensional shapes out of the standard model, doesn't mean there's missing particles we can't account for.... probably...
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... wat.
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