  Our main focus is to explore different models in noncommutative spaces in
higher dimensions. We provide a procedure to relate a three dimensional
q-deformed oscillator algebra to the corresponding algebra satisfied by
canonical variables describing non-commutative spaces. The representations for
the corresponding operators obey algebras whose uncertainty relations lead to
minimal length, areas and volumes in phase space, which are in principle
natural candidates of many different approaches of quantum gravity. We study
some explicit models on these types of noncommutative spaces, first by
utilising the perturbation theory, later in an exact manner. In many cases the
operators are not Hermitian, therefore we use PT -symmetry and
pseudo-Hermiticity property, wherever applicable, to make them self-consistent.
Apart from building mathematical models, we focus on the physical implications
of noncommutative theories too. We construct Klauder coherent states for the
perturbative and nonperturbative noncommutative harmonic oscillator associated
with uncertainty relations implying minimal lengths. In both cases, the
uncertainty relations for the constructed states are shown to be saturated and
thus imply to the squeezed coherent states. They are also shown to satisfy the
Ehrenfest theorem dictating the classical like nature of the coherent
wavepacket. The quality of those states are further underpinned by the
fractional revival structure. More investigations into the comparison are
carried out by a qualitative comparison between the dynamics of the classical
particle and that of the coherent states based on numerical techniques. The
qualitative behaviour is found to be governed by the Mandel parameter
determining the regime in which the wavefunctions evolve as soliton like
structures.
