  In this paper, we show that the quantum bound state problems are mapped to
$N$ point vortices with the identical circulation or strength using the
Steiljes electrostatic model with imaginary charges. We also show that these
$N$ point charges or vortices, become imaginary, in a constant background field
will admit a wave solution under paraxial wave approximation. Therefore, in
quantum mechanics as long as paraxial approximation is valid it behaves like a
wave.
