Duality between the coordinates and wave functions on noncommutative space

TL;DR

This paper explores the relationship between coordinates and wave functions in noncommutative space, deriving a specific relation for certain wave functions and analyzing the differential equations governing quantum prepotentials.

Contribution

It establishes a duality between coordinates and wave functions in noncommutative space and derives the differential equations for quantum prepotentials.

Findings

Derived the relation between coordinates and wave functions in noncommutative space.

Identified the class of wave functions with linearly dependent quantum prepotentials.

Presented the differential equation satisfied by the quantum prepotentials.

Abstract

The relation between coordinates and the solutions of the stationary Schrodinger equation in the noncommutative algebra of functions on $R^{2N}$ is discussed. We derive this relation for a certain class of wave functions for which the quantum prepotentials depend linearly on the coordinates similarly to the commutative case. Also, the differential equation satisfied by the prepotentials is given.