(2+2)–dimensional quantum mechanical q–phase space which is the semi– direct product of the quantum planeEq(2)/U(1) and its dual algebra eq(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ”Quantum mechanical q–Hamiltonian” of the motion over the quantum plane is derived and the solution of the Schrödinger equation for the q– semiclassical motion governed...

Using microfabrication techniques, it has become possible to make mechanical devices with dimensions in the micro and even in the nano scale domain. Allied to low temperature techniques, these systems have opened a new path in physics with the ultimate goal of reaching the quantum nature of a macroscopic mechanical degree of freedom1. Within this field, materials research plays a significant ro...

Quantum mechanically, there is a key difference. Consider the quantum mechanical equivalent of coin-tossing, namely letting an electron (or photon) “go through” a two-slit screen, with two detectors placed close to the screen on the other side. One and only one of the detectors will always fire. The top (bottom) detector firing would be the quantum mechanical equivalent of heads (tails). Quantu...

Quantum capacitance is a fundamental quantity that can directly reveal many-body interactions among electrons and is expected to play a critical role in nanoelectronics. One of the many tantalizing recent physical revelations about quantum capacitance is that it can possess a negative value, hence allowing for the possibility of enhancing the overall capacitance in some particular material syst...

A quantum mechanical search procedure to determine the real zeros of a polynomial is introduced. It is based on the construction of a spin observable whose eigenvalues coincide with the zeros of the polynomial. Subsequent quantum mechanical measurements of the observable output directly the numerical values of the zeros. Performing the measurements is the only computational resource involved. P...