Molecular beam epitaxy has led to quantum wells which confine electrons and holes in one direction and microcavities which confine photons in one direction. In this proposal, 2D and 3D confinement of electrons is studied by using a magnetic field of up to 14 Tesla to quantize the quantum-well energy levels in one or both of the directions perpendicular to the direction of growth of the semiconductor cavity. By applying no field, a field parallel to the layers, and a field perpendicular to the lasers it is proposed to compare carrier relaxation and microcavity lasing for quantum wells, quantum wires and quantum dots, respectively, using the same quantum well and microcavity. Although fundamentally conceived and oriented, this research is strategic for manufacturing of low- threshold microlasers for use in the information superhighway, optical data storage, large panel displays, etc.