A spin-dependent quantum trajectory methodology is outlined which achieves electron exchangecorrelation on an ab initio basis. The methodology is intended to give workers in electronic structure the same computational capability which has been available for decades in classical dynamics.

Abstract:
this paper presents a computational model of electrons dynamics and gain in four-level two-electron atomic systems. these systems, submitted to an electromagnetic wave, are governed by pauli exclusion principle and they are modeled using the time-domain transmission line matrix (tlm) method with the symmetrical condensed node (scn) with novel voltage sources. the development of the proposed model is based on the incorporation, in maxwell's equations, of the coupled rate equations with pauli exclusion principle, taking into account the dynamic pumping in the tlm formulation. the scattering matrix characterizing the scn with the new voltage sources is provided and the numerical results are compared with those of the literature or with the theoretical ones.

A quantum
theory for a one-electron system can be developed in either Heisenberg picture
or Schrodinger picture. For a many-electron system, a theory must be developed
in the Heisenberg picture, and the indistinguishability and Pauli’s exclusion
principle must be incorporated. The hydrogen atom energy levels are obtained by
solving the Schrodinger energy eigenvalue equation, which is the most significant
result obtained in the Schrodinger picture. Both boson and fermion field
equations are nonlinear in the presence of a pair interaction.

Abstract:
In this report, different models of bonding and structure such as Lewis, VSEPR, Ligand close packing (LCP), VB, qualitative MO and QTAIM have been applied to analyze the Bonds and structures of two equilibrium geometries (planar D_{2h} and perpendicular D_{2d}) of C_{2}H_{4}^{2+}. The geometries were optimized at near RHF and MP2 limit using ccpVTZ basis set. While the above bonding models are successfully applied for predicting the low energy isomers of molecules, prior to solving the Schr?dinger equation, it is shown that the cited models fail in predicting the existence of perpendicular, D_{2d} form of C_{2}H_{4}^{2+}. In this regard the interpretations of significant energetic stabilization of D_{2d} form over planar isomer has also been revisited. This is attributed to the hidden effect of the Pauli Exclusion principle.

Abstract:
in this paper, the first of a series, a historical overview of the conceptual development of the old atomic theory is sketched, ranging from bohr's first model for atomic structure, in 1913, to the proposal of the exclusion principle by pauli, in 1925. initially, arguments are given that aim to establish the validity and the relevance of a study of a research program such as the old atomic theory, and an attempt is made to put that program in context within the framework of quantum theory in general. next, one discusses topics such as: the structure of atomic spectra, the status of the correspondence principle, sommerfeld's general quantum condition in terms of phase integrals, the elliptic-relativistic model of the atom, the bohr-kramers-slater theory of radiation, kramer's theory of dispersion, the concept of spin, the problem of the electronic configuration of atoms, and the structure of the periodic table, among others. an effort is made to present a history that highlights the inter-relations between concepts, and ample reference is made both to the primary sources and to the relevant secondary literature. the historical overview thus developed will serve as a basis for a second, forthcoming paper, in which imre lakatos' reading of the old atomic theory will be critically analyzed. although prepared originally with a view to serving as a reference for the ensuing paper, the present text can also be read in an autonomous way, functioning as a brief (and by no means exhaustive) historical introduction to this important and fascinating period of twentieth century physics.

Abstract:
叙述泡利不相容原理发现的整个过程，给出了泡利不相容原理在近代物理中的三个重要的应用，确立同科电子的原子态，氦原子能级之谜和费米–狄拉克统计。
We introduce the discovery process of Pauli Exclusion Principle, and present three important applications, i.e., derivation of atomic states of equivalent electrons, the mystery of helium atom energy levels and Fermi-Dirac dis- tribution.

Abstract:
in this paper, taking as a starting point the historical panorama sketched in the first article of this series (bezerra, 2003), i undertake a critical analysis of the reconstruction of the early atomic theory performed by imre lakatos (1970), and show it to be inadequate in several respects. the present text begins by an exposition of lakatos' model, the so-called methodology of scientific research programmes. the main problems confronting the lakatosian reconstruction are then discussed, referring to aspects such as: the status of the correspondence principle; the omission of sommerfeld's quantization condition; the omission of various important developments occurred in the period 1921-1924; and the unsatisfactory treatment given to the concept of spin. the main difficulty confronting a reconstruction of lakatosian type, however, refers to the bohr-kramers-slater theory of radiation (bks) and to kramers' theory of dispersion which are mostly ignored by lakatos, but are discussed here in detail. as a result of such problems, the lakatosian account of the "degenerating phase" of the early atomic theory is itself seriously called into question. in the closing section of the paper, one is led to conclude that some of the difficulties are of a historiographical nature, resulting basically from a bad application of the model; others, however, point to a deeper inadequacy of the methodology of research programmes itself. towards the end, the possible causes of such inadequacy are discussed including, in particular, the lakatosian concept of the hard core of a research program, and the unsatisfactory analysis of the conceptual aspects of science and possible paths for their overcoming are suggested.

In this paper, we extend the
definition of Boolean canalyzing functions to the canalyzing functions of
multi-state case. Namely, f:Q^{n}→Q, where Q={a_{1},a_{2},...,a_{q}}. We obtain its cardinality
and the cardinalities of its various subsets (They may not be disjoint). When q=2, we obtain a combinatorial
identity by equating our result to the formula in [1]. For a better
understanding to the magnitude, we obtain the asymptotes for all the
cardinalities as either n→∞ or q→∞.

We all physicist have long been believed that an elementary particle is a wave as well as a particle, but we discuss in this paper that an electron (probably all fermions) is always a particle. Author claim that quantum mechanics (QM) is not such mysterious as Bohr stated that the wave turn to the particle by observation. We can understand QM by natural human sense. The wave nature of electrons is only an appearance or a phenomena but not intrinsic or substantial. An electron is an individual body, which interferes with other individual electrons. Interference is the key word instead of the wave to understand the quantum mechanics. Interference produces the wave nature and the uncertainty. When we determine that an electron is nothing but a particle, we will see the true meaning of wave function and the Schr?dinger’s equation.

Most periodic tables of the chemical elements are
between 96% and 100% in accord with quantum mechanics. Three elements only do
not fit correctly into the official tables, in disagreement with the spherical
harmonics and the Pauli exclusion principle. Helium, belonging to the s-block,
should be placed beside hydrogen in the s-block instead of the p-block.
Lutetium and lawrencium belonging to the d-block of the
transition metals should not be in the f-block of the
lanthanides or the actinoids. With these slight modifications, the IUPAC table
becomes quantum mechanics consistent.