A pedagogical review on supersymmetry in quantum mechanis is presented which provides a comprehensive coverage of the subject. First, the key ingredients on the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltotian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. We also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N=1 and N=2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. We treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called ‘shape-invariance’ of potentials. To make transparent the relationship between supersymmetry and solvable potentials, we also solve several examples. We then go over to the formulation of supersymmetry in radial problems, paying a special attention to the Coulomb and isotropic oscillator potentials. We show that the ladder operator technique may be suitably modified in higher dimensions for generating isospectral Hamiltonians. Next, the criteria for the breaking of supersymmetry is considered and their range of applicability is examined by suitably modifying the definition of Witten’s index. Finally, we perform some numerical calculations for a class of potentials to show how a modified WKB approximation works in supersymmetric cases.

It is shown that the eigenvalue problem of the L operator for the sine-Gordon equation can be put in a supersymmetric form. We comment on the connection between the conserved quantities of the Korteweg-de Vries and sine-Gordon systems.Perhaps the simplest of all integrable systems is the Korteweg-de Vries (KdV) equation

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We have examined the saturation of anomalous Ward identities by the low-lying pseudoscalars TO, 7, and 7' to determine the sizes of 7'-7, TO-^, and TO-7' mixing angles. The 7'-7 mixing angle turns out to be about -20" which is consistent with the recent findings. Our estimate for the aO-7 mixing angle shows that it could be bigger than the older value obtained from the p-w mixing, baryon mass splittings, and kaon mass difference.