Heisenberg's uncertainty relations have played an essential role in quantum physics since its very beginning. The uncertainty relations in the modern quantum formalism have become a fundamental limitation on the joint measurements of general quantum mechanical observables, going much beyond the original discussion of the trade-off between knowing a particle's position and momentum. Recently, th...

The spectrum of the perturbed polyharmonic operator H = (−∆)l + V in L(Rd) with a limit-periodic potential V is studied. It is shown that if V is periodic in one direction in Rd and 8l > d+3, d = 1(mod4), then the spectrum of H contains a semiaxis. The proof is based on the properties of periodic operators. §

We survey various origins and expressions for the quantum potential, expanding and extending the treatment given in a previous paper [35].

We show that given an essentially arbitrary Q(x, t, ~) there are “generalized” quantum theories having Q as their quantum potential.

A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a smoothed potential both of them constructed from the classical potential. The exact solution of the approximated theory in one spatial dimension is found. The con...

We formulate according to the quantum mechanical uncertainty relation a new uncertainty relation ∆ ˘ A · ∆l ∼ ¯ h e where ˘ A and ∆l ≥ l B are the electromagnetic pure gauge potential, the position uncertainty and the magnetic length, respectively. Then, we show that the observed potential drops on the edge of QHE samples are varifications of this uncertainty relation, where the quantum potenti...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...