1304.5735 (K V S Shiv Chaitanya)

Stieltjes Electrostatic Model Interpretation for Bound State Problems    [PDF]

K V S Shiv Chaitanya

In this paper, we have shown the duality between the Stieltjes electrostatic interpretation for zeros of orthogonal polynomials and the quantum Hamilton Jacobi formalism. From this duality, one can view the bound state problem as $n$ unit moving imaginary charges $i\hbar$, which are placed in between the two fixed imaginary charges arising due to the classical turning points of the potential. The interaction potential between $n$ unit moving imaginary charges $i\hbar$ is given by logarithm of the wave function. For an exactly solvable potential, this system attains stable equilibrium position at the zeros of the orthogonal polynomials polynomial depending upon the interval of the classical turning points.

View original: http://arxiv.org/abs/1304.5735