相关论文: Generalized Continuity Equation and Modified Norma…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
At large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in…
It is shown that in the model [3,4] of quantum mechanics besides probability amplitudes, the Planck constant and the Fock space, the cosmological constant also appear in the natural way. The Poisson brackets are generalized for the case of…
In this paper, we study implications of the geometrical nature of space- time for some of the basic tenets of quantum mechanics. That is, we study two different implications of the principle of general covariance; first we quantize a…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
The treatment of time in relativity does not conform to that in quantum theory. To resolve the discrepancy, a formalization of time is introduced in an accompanying paper, starting from the assumption that the treatment of time in physics…
Extended quantum mechanics using non-Hermitian, pseudo-Hermitian Hamiltonians is briefly reviewed. Supersymmetric regularizations, solvable simulations and large-N expansion techniques are recollected as suitable means for the study of…
One brief idea on the extended uncertainty relation and the dynamical quantization of space-time at the Planck scale is presented. The extended uncertainty relation could be a guiding principle toward the renormalizable quantum gravity.…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of…
Noether's theorem is one of the fundamental laws in physics, relating the symmetry of a physical system to its constant of motion and conservation law. On the other hand, there exist a variety of non-Hermitian parity-time (PT)-symmetric…
The quantum mechanics status of the probability vector current density has long seemed to be marginal. On one hand no systematic prescription for its construction is provided, and the special examples of it that are obtained for particular…
We extend previous work on the arrival time problem in quantum mechanics, in the framework of decoherent histories, to the case of a particle coupled to an environment. The usual arrival time probabilities are related to the probability…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
We suggest a general ansatz for the energy-eigenstates when a complex one-dimensional PT-symmetric potential possesses real discrete spectrum. Several interesting features of PT-symmetric quantum mechanics have been brought out using this…
We revisit an argument proposed by Hardy \cite{Hardy-1} concerning local realistic theories, but in terms of the motion of the probability fluid and its current within standard quantum mechanic. We emphasize surprising properties of the…
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…