Quantum mechanics of a particle in an accelerated frame and the equivalence principle

We study the effect of acceleration of a uniformly accelerated frame on the free-particle dynamics in a quantum domain. Specifically we demonstrate how the behaviour of a free quantum particle, as observed by an observer with uniform acceleration, completely changes from that of a quantum particle immersed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen from a frame with uniform acceleration.