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We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb…
Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic…
We argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the freezing of vacuum energy in such a dynamical energy-momentum space and present a…
The scaling of neutral atoms to large $Z$, combining periodicity with a gradual trend to homogeneity, is a fundamental probe of density functional theory, one that has driven recent advances in understanding both the kinetic and…
Energy is no doubt an intuitive concept. Following a previous analysis on the nature of elementary particles and associated elementary quantum fields, the peculiar status and role of energy is scrutinised further at elementary and larger…
For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…
A system of two initially homogeneous, physically real fields uniformly attracted to each other is considered as the simplest basis of the self-developing world structure. It is shown that the system is unstable against periodic cycles of…
The prevalent role of force in traditional quantum mechanics is outlined, with special reference to approximate calculations for stationary states. It will be explored how far this force concept can be made useful in the concerned area. The…
A new model of quantum mechanics, Classical Quantum Mechanics, is based on the (nearly heretical) postulate that electrons are physical objects that obey classical physical laws. Indeed, ionization energies, excitation energies etc. are…
We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and…
The invariant mass of free particles is used to derive a bound-state equation for the hydrogen atom at rest. This equation has the well-known solutions for the single-particle states. Existence of two-particle bound states, for which the…
A quantum kinetic theory for correlated charged-particle systems in strong time-dependent electromagnetic fields is developed. Our approach is based on a systematic gauge-invariant nonequilibrium Green's functions formulation. Extending our…
When the Zeeman energy approaches the characteristic kinetic energy of electrons, Landau quantization becomes important. In the vicinity of magnetars, the Zeeman energy can even be relativistic. We start from the Dirac equation and derive a…
Energy densities of the quantum states that are superposition of two multi-electron-positron states are examined. It is shown that the energy densities can be negative only when two multi-particle states have the same number of electrons…
We define the state of minimum energy while the expectation values of the field operators and their time derivatives in a determined moment in such a state are constrained. As an axiom, we consider such a state as the background of the…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
We consider the so-called semiclassical variant of general relativity, where gravitational field is not quantized but matter is quantized, for the simplest composite quantum body - a hydrogen atom. We create a stationary electron quantum…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
Interactions never lower the ground state kinetic energy of a quantum system. However, at nonzero temperature, where the system occupies a thermal distribution of states, interactions can reduce the kinetic energy below the noninteracting…
We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in semiclassical variant of general relativity, where gravitational field is not quantized but matter is quantized. To…