Related papers: Schrodinger equation from an exact uncertainty pri…
Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the…
The transition from classical physics to quantum mechanics has been mysterious. Here, we derive the space-independent von Neumann equation for electron spin mathematically from the classical Bloch or Majorana--Bloch equation, which is also…
In 1927 Heisenberg discovered that the ``more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa''. Four years later G\"odel showed that a finitely specified, consistent formal…
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position…
Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism…
The wave function of quantum mechanics is not a boost invariant and gauge invariant quantity. Correspondingly, reference frame dependence and gauge dependence are inherited to most of the elements of the usual formulation of quantum…
An interesting phenomenon is happening in the construction of the Madelung equations from the Schrodinger equation. It seems like the Madelung equations require a rotational invariance symmetry to properly account for quantum vortices, and…
Recently we showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p=\partial_q S_0 and exploits a basic GL(2,C)-symmetry which…
Uncertainty relations are shown to have nothing specific for quantum mechanics, being the general property valid for arbitrary function. A wave function of a particle having precisely defined position and momentum in QM simultaneously is…
Classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
The question about the appearance of time in the semiclassical limit of quantum gravity continues to be discussed in the literature. It is believed that a temporal Schrodinger equation for matter fields on the background of a classical…
Arguments are gived for the plausibility that quantum mechanics is a stochastic theory and that many quantum phenomena derive from the existence of a real noise consisting of vacuum fluctuations of all fundamental fields existing in nature.…
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We…
Despite the unparalleled accuracy of quantum-theoretical predictions across an enormous range of phenomena, the theory's foundations are still in doubt. The theory deviates radically from classical physics, predicts counterintuitive…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
We give a new proof of Hardy's uncertainty principle, up to the end-point case, which is only based on calculus. The method allows us to extend Hardy's uncertainty principle to Schr\"odinger equations with non-constant coefficients. We also…
There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…