Double Shell Structure of the Periodic System of the Elements

1970 ◽  
Vol 25 (2) ◽  
pp. 210-217 ◽  
Author(s):  
D. Neubert
Keyword(s):  
Schrödinger Equation ◽  
Quantum Number ◽  
Periodic System ◽  
Shell Structure ◽  
Schrodinger Equation ◽  
The Other ◽  
Coulomb Problem ◽  
Other Hand ◽  
Partial Filling ◽  
Symmetry Properties

Abstract A new periodic system of the elements (PSE) is proposed which exhibits symmetry properties not apparent in the conventional arrangement of the elements. By discussing the solutions of the non-relativistic Schrödinger equation for the Coulomb problem it is shown that the PSE might be based on the filling of only four Coulomb shells as compared to the partial filling of up to eight shells in the conventional classification. On the other hand, the multiplicity of the states in the PSE appears to be four as compared to two due to spin in the hydrogen spectrum. A transformation of the PSE-spectrum into the hydrogen spectrum is possible by a rotation in quantum number space.

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

Three and Four Centre Oscillators and Their Application in Nuclear Physics

1974 ◽  
Vol 29 (7) ◽  
pp. 1003-1010 ◽  
Author(s):  
Peter Bergmann ◽  
Hans-Joachim Scheefer
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Nuclear Physics ◽  
Schrodinger Equation ◽  
Numerical Procedure ◽  
Orthogonal Basis ◽  
Two Dimensional ◽  
Schmidt's Method ◽  
Symmetry Properties

The extension of the nuclear two-centre-oscillator to three and four centres is investigated. Some special symmetry-properties are required. In two cases an analytical solution of the Schrödinger equation is possible. A numerical procedure is developed which enables the diagonalization of the Hamiltonian in a non-orthogonal basis without applying Schmidt's method of orthonormalization. This is important for calculations of arbitrary two-dimensional arrangements of the centres.

scholarly journals Calculation of Binding Energy and Wave Function for Exotic Hidden-Charm Pentaquark

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
F. Chezani Sharahi ◽  
M. Monemzadeh
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
The Other

In this study, pentaquark P c 4380 composed of a baryon Σ c , and a D ¯ ∗ meson is considered. Pentaquark is as a bound state of two-body systems composed of a baryon and a meson. The calculated potential will be expanded and replaced in the Schrödinger equation until tenth sentences of expansion. Solving the Schrödinger equation with the expanded potential of Pentaquark leads to an analytically complete approach. As a consequence, the binding energy E B of pentaquark P c and wave function is obtained. The results E B will be presented in the form of tables so that we can review the existence of pentaquark P c . Then, the wave function will be shown on diagrams. Finally, the calculated results are compared with the other obtained results, and the mass of observing pentaquark P c and the radius of pentaquark are estimated.

scholarly journals Schrödinger Equations in Electromagnetic Fields: Symmetries and Noncommutative Integration

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1527
Author(s):  
Alexey Anatolievich Magazev ◽  
Maria Nikolaevna Boldyreva
Keyword(s):  
Schrödinger Equation ◽  
Electromagnetic Fields ◽  
Schrodinger Equation ◽  
Symmetry Algebra ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Exact Integration ◽  
First Order ◽  
Symmetry Properties ◽  
Noncommutative Integration

We study symmetry properties and the possibility of exact integration of the time-independent Schrödinger equation in an external electromagnetic field. We present an algorithm for constructing the first-order symmetry algebra and describe its structure in terms of Lie algebra central extensions. Based on the well-known classification of the subalgebras of the algebra e(3), we classify all electromagnetic fields for which the corresponding time-independent Schrödinger equations admit first-order symmetry algebras. Moreover, we select the integrable cases, and for physically interesting electromagnetic fields, we reduced the original Schrödinger equation to an ordinary differential equation using the noncommutative integration method developed by Shapovalov and Shirokov.

scholarly journals Degradation of Si/Ge core/shell nanowire heterostructures during lithiation and delithiation at 0.8 and 20 A g−1

Nanoscale ◽  
2018 ◽  
Vol 10 (16) ◽  
pp. 7343-7351 ◽  
Author(s):  
Dongheun Kim ◽  
Nan Li ◽  
Chris J. Sheehan ◽  
Jinkyoung Yoo
Keyword(s):  
Lithium Ion Battery ◽  
Shell Structure ◽  
Lithium Ion ◽  
The Other ◽  
Core Shell ◽  
Rate Dependent ◽  
Charging Rate ◽  
Other Hand ◽  
Nanowire Heterostructures ◽  
Core Shell Structure

The charging rate-dependent degradation of lithium ion battery anodes based on Si/Ge core/shell nanowire heterostructure was observed. Si/Ge core/shell structure was preserved at the charging rate of 0.8 A g−1. On the other hand, compositional intermixing and loss of Si occurs at the charging rate of 20 A g−1.

On the Possible Electronic Structure of Atoms in a Space of Higher Dimension

2018 ◽  
pp. 222-238
Keyword(s):  
Schrödinger Equation ◽  
Quantum Number ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Principal Quantum Number ◽  
Higher Dimension ◽  
Quantum Numbers ◽  
Spin Quantum ◽  
Spin Quantum Number ◽  
Quantum Cells

It is shown that the stationary Schrödinger equation describing the distribution of electrons in the vicinity of the atomic nucleus has a solution, in principle, for any dimensionality of the space around the nucleus. As an example, a solution of the Schrödinger equation in a five - dimensional space is obtained. It is shown that the solution of the Schrödinger equation in p - dimensional space has p quantum numbers: the principal quantum number, the orbital quantum number and p - 2 magnetic quantum numbers. Taking into account the spin quantum number, the total number of quantum numbers in p - dimensional space is p + 1. This leads to the possibility of increasing the number of quantum cells of orbitals and, consequently, to the possibility of increasing the valence of the elements.

scholarly journals Quantum Energy of a Particle in a Finite-potential Well Based Upon Golden Metric Tensor

2019 ◽  
pp. 1-9
Author(s):  
I. I. Ewa ◽  
S. X. K. Howusu ◽  
L. W. Lumbi
Keyword(s):  
Quantum Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Particle Energy ◽  
The Other ◽  
Laplacian Operator ◽  
Potential Well ◽  
Metric Tensor ◽  
Quantum Energy

In our previous work titled “Riemannian Quantum Theory of a Particle in a Finite-Potential Well", we constructed the Riemannian Laplacian operator and used it to obtain the Riemannian Schrodinger equation for a particle in a finite-potential well. In this work, we solved the golden Riemannian Schrodinger equation analytically to obtain the particle energy. The solution resulted in two expressions for the energy of a particle in a finite-potential well. One of the expressions is for the odd energy levels while the other is for the even energy levels.

Carbonation Front Progress in Mortars Containing Fly Ash Considering the Presence of Chloride Ions

2014 ◽  
Vol 634 ◽  
pp. 214-221 ◽  
Author(s):  
Raphaele Malheiro ◽  
Aires Camões ◽  
Rui Miguel Ferreira ◽  
Gibson Meira ◽  
Teresa Amorim ◽  
...  
Keyword(s):  
Fly Ash ◽  
Moisture Content ◽  
Chloride Ions ◽  
Chloride Penetration ◽  
The Other ◽  
Other Hand ◽  
Partial Filling ◽  
Nacl Concentration ◽  
The Matrix ◽  
Combined Action

The incorporation of fly ash (FA) in cementitious matrices have been frequently used in order to make the matrix more resistant to the action of chlorides. On the other hand, it is known that Ca (OH)2 existing in the matrix is partially consumed by the pozzolanic reactions, which facilitates the advancement of carbonation. Given that the combined action between carbonation and chloride penetration is a fact little known, we speculate about the behaviour of the matrix in this context. This study investigates the influence of the presence of chlorides on the carbonation in mortars with FA. Samples with 0% and 40% replacement of cement CEM I 42.5 R for FA were molded with water/binder 0.56 and 0.52 respectively. After 90 days of curing the specimens were subjected to cycles of immersion/drying for 56 days. Half of the samples was subjected to the following cycle: two days in a solution containing NaCl (concentration equal to 3.5 %); 12 days in the carbonation chamber (4% of CO2). The other half was: two days in water; 12 days in the carbonation chamber. Then, the development of carbonation was evaluated. The results indicate that the presence of chlorides influences the carbonation. The specimens submitted to the exclusive action of CO2 showed a greater depth of carbonation compared to that presented by the specimens subjected to combined action. This may be related to changes in properties of the matrix which may lead to further refinement of the pores and related to the presence of the salt that can lead to partial filling of the pores and the increase in moisture content .

Etude à basse température des largeurs et des déplacements des raies rovibrationnelles de la bande fondamentale de H35Cl comprimé par N2, O2, D2 et H2

1980 ◽  
Vol 58 (3) ◽  
pp. 318-324 ◽  
Author(s):  
J. P. Houdeau ◽  
M. Larvor ◽  
C. Haeusler
Keyword(s):  
Quantum Number ◽  
Satisfactory Agreement ◽  
Electrostatic Interactions ◽  
Rotational Quantum Number ◽  
The Other ◽  
Realistic Approach ◽  
Other Hand ◽  
Different Temperatures ◽  
And Shifts

Linewidths and shifts in the spectrum (v0→1 band) of H35Cl perturbed by N2, O2, D2, and H2 have been measured for different temperatures (at 298 and 163 K). The Sisam spectrometer resolution was 0.024 cm−1. The Anderson–Tsao–Curnutte theory has been applied to the linewidth calculations. For perturbation by N2 and O2, this approach is justified by the intensity of electrostatic interactions, and it leads to a satisfactory agreement with experiment, at least for lines of low rotational quantum number. On the other hand, the low value of H2 and D2 quadrupole leads to values of the optical diameter close to the kinetic diameter. A discussion shows then that a more realistic approach is needed in that case.[Journal translation]

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