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We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy…
It is shown that passive gravitational mass operator of a hydrogen atom in the post-Newtonian approximation of the general relativity does not commute with its energy operator, taken in the absence of gravitational field. Nevertheless, the…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
The dynamics is investigated of a free particle on a sphere (rigid rotor or rotator) that is initially in a coherent state. The instability of coherent states with respect to the free evolution leads to nontrivial time-development of…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
The total energy of a quasi-one-dimensional electron system is calculated using density functional theory. It is shown that spontaneous ferromagnetic state in quantum wire occurs at low one-dimensional electron density. The critical…
Momentum is analyzed as a random variable in stochastic quantum mechanics. Arbitrary potential energy functions are considered. The oscillator is presented as an example.
A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical…
The simplest quantum composite body, a hydrogen atom, is considered in the presence of a weak external gravitational field. We define an operator for the passive gravitational mass of the atom in the post-Newtonian approximation of the…
Quantum algorithms for estimating the ground state energy of a quantum system often operate by preparing a classically accessible quantum state and then applying quantum phase estimation. Whether this approach yields quantum advantage…
The basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac $\delta$-$\delta^\prime$ functions or a specific potential with extended compact support are…
We obtain an exact formula for the equilibrium free energy of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a heat bath of independent quantum harmonic…
The concept of elementary particle rests on the idea that it is a physical system with no excited states, so that all possible kinematical states of the particle are just kinematical modifications of any one of them. The way of describing…
An accurate expression of the kinetic energy density of an electronic distribution in terms of the single particle reduced density matrix for atomic and molecular systems is a long-standing problem in electron structure theory. Existing…
The total energy of the ground state of the quantum harmonic oscillator is obtained with minimal assumptions. The vacuum energy density of the universe is derived and a cutoff frequency is obtained for the upper bound of the quantum…
Using a combination of semiclassical and recently developed wave packet propagation techniques we find the quantum self-ionization process of highly excited ions moving in magnetic fields which has its origin in the energy transfer from the…
We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for…
For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent…
Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high temperature…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…