Electron’s Position Expectation Values and Energy Spectrum of Lithium Ion (Li^(2+)) on Principal Quantum Number n≤3

The purpose of this study is to determine the electron’s position expectation values and energy spectrum on the Li2+ ion on the principal quantum number n≤3. This research using literature study methods on quantum mechanics. The expectation values of the electron position and the energy spectrum of the Li2+ ion uses numerical calculations using the Matlab 2019a program. The steps in this research method include: preparation; theory development; simulation; validation of the results of theory development; results of theory development; discussion and conclusion. The results obtained in this study are the electron’s position expectation values and energy of the Lithium ion. The electron’s position expectation values indicates the presence of electrons that often appear around the x-axis by relying on the interval used. The larger the interval, the more constant the electron’s position expectation values will be and towards an almost constant value. From the analysis results, the expectation value varies in positions from 0,0001a0 to 0,1637a0. The electron energy spectrum of the Li2+ ion is inversely proportional to the square of the principal quantum number (n),E1= -122,4 eV ; E2= -30,6 eV ; E3= -13,6 eV

Колебательно-вращательный спектр высокого разрешения в районе полос 3ν-=SUB=-4-=/SUB=-, ν-=SUB=-2-=/SUB=-+2ν-=SUB=-4-=/SUB=- и 2ν-=SUB=-2-=/SUB=-+ν-=SUB=-4-=/SUB=- молекулы -=SUP=-72-=/SUP=-GeH-=SUB=-4-=/SUB=-

The high-resolution spectrum of the 72GeH4 molecule was recorded on a Bruker IFS 125HR Fourier spectrometer with an optical resolution of 0.003 cm-1. The line positions were analyzed for ten interacting vibrational-rotational bands 3ν4 (1F2, F1, 2F2), v2+ 2ν4 (1E, F1, F2, 2E) and 2ν2+v4 (1F2, F1, 2F2) in the range 2350-2750 cm-1. As a result of the analysis, 1726 experimental lines were identified with the maximum value of the quantum number Jmax = 17; then used in the fitting procedure with parameters of the effective Hamiltonian. The resulting set of 35 spectroscopic parameters describes the vibrational-rotational structure of the spectrum with drms = 7.5 · 10-4 cm-1.

Power-like potentials: From the Bohr–Sommerfeld energies to exact ones

For one-dimensional power-like potentials [Formula: see text], [Formula: see text], the Bohr–Sommerfeld energies (BSE) extracted explicitly from the Bohr–Sommerfeld quantization condition are compared with the exact energies. It is shown that for the ground state as well as for all positive parity states the BSE are always above the exact ones as opposed to the negative parity states where the BSE remain above the exact ones for [Formula: see text] but below them for [Formula: see text]. The ground state BSE as function of [Formula: see text] are of the same order of magnitude as the exact energies for linear [Formula: see text], quartic [Formula: see text] and sextic [Formula: see text] oscillators but their relative deviation grows with [Formula: see text], reaching the value 4 at [Formula: see text]. For physically important cases [Formula: see text], for the 100th excited state BSE coincide with exact ones in 5–6 figures. It is demonstrated that by modifying the right-hand side of the Bohr–Sommerfeld quantization condition by introducing the so-called WKB correction [Formula: see text] (coming from the sum of higher-order WKB terms taken at the exact energies or from the accurate boundary condition at turning points) to the so-called exact WKB condition one can reproduce the exact energies. It is shown that the WKB correction is a small, bounded function [Formula: see text] for all [Formula: see text]. It grows slowly with increasing [Formula: see text] for fixed quantum number [Formula: see text], while it decays with quantum number growth at fixed [Formula: see text]. It is the first time when for quartic and sextic oscillators the WKB correction and energy spectra (and eigenfunctions) are found in explicit analytic form with a relative accuracy of [Formula: see text] (and [Formula: see text]).

Newly observed X(4630): a new charmoniumlike molecule

Very recently, the LHCb Collaboration at the Large Hadron Collider at CERN observed new resonance X(4630). The X(4630) is decoded as a charmoniumlike molecule with hidden-strange quantum number well in the one-boson-exchange mechanism. Especially, the study of its hidden-charmed decays explicitly shows the dominant role of $$J/\psi \phi $$ J / ψ ϕ among all allowed hidden-charmed decays of the X(4630), which enforces the conclusion of X(4630) as a charmoniumlike molecule. The discovery of the X(4630) is a crucial step of constructing charmoniumlike molecule zoo.

Consideration of Additive Quantum Numbers of Fermions and Their Conservations

Two new flavor quantum numbers D and U for down and up quarks, respectively, are introduced, and then quark quantum number H is proposed as the sum of the flavor quantum numbers of quarks. Moreover, lepton quark-like quantum number HL and finally fermion quantum number F are brought forward. Old and new additive quantum numbers are conserved at three different levels in weak interaction, and F builds up a clear relationship to the electric charge of fermions.

Calculation of Maximal Number of Areas of Longitudinal Periodic Localization of Drifting Electrons in Metallic Explorer with Electric Current of Conductivity

The results of approximate calculation of the maximal value of the quantum number of n = nm for the quantized standing longitudinal electronic de Broglie half-waves λezn/2 = l0/n long and, accordingly, of the maximal number of nm of the quantized areas of the longitudinal periodic localization with the length of Δznh of drifting lone electrons in the cylindrical explorers of eventual sizes (long l0 and radius of r0) with the axial-flow current of conductivity of i0(t) of the indicated kinds and peak-temporal parameters (PTP) are presented, taking into account the quantum-wave nature of the electric current of conductivity of i0(t) of different kinds (permanent, variable, and impulsive) and PTP in the metallic explorers. The results of verification of the obtained calculations of the quantum-mechanical correlation for the determination of the quantum number nm confirm its possibility to be applied in such areas of engineering as high-voltage heavy-current impulsive technique and electrophysical treatment of metals by a strong electromagnetic field and by a pressure of a large impulsive current.