Related papers: On a paradox in quantum mechanics and its resoluti…

Employing very simple electro-mechanical principles known from classical physics, the Kibble balance establishes a very precise and absolute link between quantum electrical standards and macroscopic mass or force measurements. The success…

The Quantum Ergodic Conjecture equates the Wigner function for a typical eigenstate of a classically chaotic Hamiltonian with a delta-function on the energy shell. This ensures the evaluation of classical ergodic expectations of simple…

We demonstrated that classical mechanics have, besides the well known quantum deformation, another deformation -- so called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit $h\to 0$ not only of the…

The variance of observables of quantum states of the Laplacian on the modular surface is calculated in the semiclassical limit. It is shown that this hermitian form is diagonalized by the irreducible representations of the modular quotient…

We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local…

We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation.…

The biorthogonal formalism extends conventional quantum mechanics to the non-Hermitian realm. It has, however, been pointed out that the biorthogonal inner product changes with the scaling of the eigenvectors, an ambiguity whose physical…

This work addresses the problem of solving the Cahn-Hilliard equation numerically. For that we introduce an abstract formulation for Cahn-Hilliard type equations with dynamic boundary conditions, we conduct the spatial semidiscretization…

We reconsider the generalization of standard quantum mechanics in which the position operators do not commute. We argue that the standard formalism found in the literature leads to theories that do not share the symmetries present in the…

We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum…

We study the variational structure of the complex $k$-Hessian equation on bounded domain $X\subset \mathbb C^n$ with boundary $M=\partial X$. We prove that the Dirichlet problem $\sigma_k (\partial \bar{\partial} u) =0$ in $X$, and $u=f$ on…

Confinement of atoms inside impenetrable (hard) and penetrable (soft) cavities has been studied for nearly eight decades. However, a unified virial theorem for such systems has not yet been found. Here we provide a general virial-like…

Bohmian mechanics solves the wave-particle duality paradox by introducing the concept of a physical particle that is always point-like and a separate wavefunction with some sort of physical reality. However, this model has not been…

We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…

We present an improved version of Berry's ansatz able to incorporate exactly the existence of boundaries and the correct normalization of the eigenfunction into an ensemble of random waves. We then reformulate the Random Wave conjecture…

For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this…

The quantum smoothing theory [Tsang, Phys. Rev. Lett. 102, 250403 (2009); Phys. Rev. A, in press (e-print arXiv:0906.4133)] is extended to account for discrete jumps in the classical random process to be estimated, discrete variables in the…

Selection of physically meaningful solutions of the Wheeler-DeWitt equation for the wavefunction in quantum cosmology, can be attained by a reduction of the theory to the sector of true physical degrees of freedom and their canonical…

A broad range of quantum optimisation problems can be phrased as the question whether a specific system has a ground state at zero energy, i.e.\ whether its Hamiltonian is frustration free. Frustration-free Hamiltonians, in turn, play a…

The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux…