Mapping a Quantum Potential to a Delta Function and the Uncertainty Principle

 In (1), an approximate method of obtaining the ground state energy is presented by mapping a Schrodinger equation with a given potential V(x) into one with delta function potential with an appropriate weight. Various examples are presented in both (1) and (2). It should be noted that although this approach yields the exact ground state energy for the oscillator it does not yield a correct answer for a particle in a box with infinite potentials at the wall. In this note, we try to investigate a possible physical argument for a mapping into a delta function and argue it is linked to the Heisenberg uncertainty principle. We also suggest that the weighting used in (1) i.e. U1= Integral (x1,x2) V(x)dx where (x1,x2) are classical turning points, should be multiplied by a constant b which ultimately cancels in the expression for the ground state energy.