  An elementary introduction is given to the subject of Supersymmetry in
Quantum Mechanics. We demonstrate with explicit examples that given a solvable
problem in quantum mechanics with n bound states, one can construct new exactly
solvable n Hamiltonians having n-1,n-2,...,0 bound states. The relationship
between the eigenvalues, eigenfunctions and scattering matrix of the
supersymmetric partner potentials is derived and a class of reflectionless
potentials are explicitly constructed. We extend the operator method of solving
the one-dimensional harmonic oscillator problem to a class of potentials called
shape invariant potentials. Further, we show that given any potential with at
least one bound state, one can very easily construct one continuous parameter
family of potentials having same eigenvalues and s-matrix. The supersymmetry
inspired WKB approximation (SWKB) is also discussed and it is shown that unlike
the usual WKB, the lowest order SWKB approximation is exact for the shape
invariant potentials. Finally, we also construct new exactly solvable periodic
potentials by using the machinery of supersymmetric quantum mechanics.
