Boundary condition determined wave functions for the ground states of one- and two-electron homonuclear molecules

1999 ◽  
Vol 111 (16) ◽  
pp. 7278-7289 ◽  
Author(s):  
S. H. Patil ◽  
K. T. Tang ◽  
J. P. Toennies
Keyword(s):  
Boundary Condition ◽  
Ground States ◽  
Wave Functions

scholarly journals Masses of fully heavy tetraquarks $$QQ {\bar{Q}} {\bar{Q}}$$ in an extended relativized quark model

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Qi-Fang Lü ◽  
Dian-Yong Chen ◽  
Yu-Bing Dong
Keyword(s):  
Quark Model ◽  
Mass Spectra ◽  
Ground States ◽  
Lhcb Collaboration ◽  
Wave Functions ◽  
Recent Measurement ◽  
Heavy Quarkonium ◽  
Radial Excitation ◽  
Broad Structure ◽  
Narrow Structure

AbstractInspired by recent measurement of possible fully charmed tetraquarks in LHCb Collaboration, we investigate the mass spectra of fully heavy tetraquarks $$QQ {\bar{Q}} {\bar{Q}}$$ Q Q Q ¯ Q ¯ in an extended relativized quark model. Our estimations indicate that the broad structure around 6.4 GeV should contain one or more ground states for $$cc {\bar{c}} {\bar{c}}$$ c c c ¯ c ¯ tetraquarks, while the narrow structure near 6.9 GeV can be categorized as the first radial excitation of $$cc {\bar{c}} {\bar{c}}$$ c c c ¯ c ¯ system. Moreover, with the wave functions of the tetraquarks and mesons, the strong decays of tetraquarks into heavy quarkonium pair are qualitatively discussed, which can be further checked by the LHCb and CMS Collaborations.

Valence-bond studies of 4-electron 3-centre bonding units. I. The π-electrons of O3, NO2−, and CH2N2

1978 ◽  
Vol 56 (8) ◽  
pp. 1093-1101 ◽  
Author(s):  
Richard D. Harcourt ◽  
Walter Roso
Keyword(s):  
Electronic Structure ◽  
Ab Initio ◽  
Valence Bond ◽  
Ground States ◽  
Wave Functions ◽  
Dipolar Cycloaddition ◽  
Cycloaddition Reactions ◽  
Electronic Mechanism ◽  
Increased Valence

Some ab-initio valence-bond wave-functions are reported for the π-electrons of the ground-states of O3, NO2−, and CH2N2. Examination of these wave-functions provides further support for the hypothesis that, for the ground-states of many electron-excess molecules, important valence-bond structures are those that are compatible with the electroneutrality principle, i.e. they carry either small or zero formal charges on each of the atoms. For O3 and CH2N2, the important valence-bond structures with zero atomic formal charges are [Formula: see text]Each of these structures has a 'long-bond' between non-adjacent atoms. The significance of 'long-bond' (or spin-paired diradical) structures for the electronic mechanism of 1,3-dipolar cycloaddition reactions is discussed and 'increased-valence' descriptions of the electronic structure of each molecule are presented. Some comments on the utility of 'increased-valence' structures are provided.

DISCUSSION OF A KNOWN SPHERICAL BASIS FOR DIRAC WAVE FUNCTIONS

2013 ◽  
Vol 28 (08) ◽  
pp. 1350022
Author(s):  
WERNER SCHEID
Keyword(s):  
Boundary Condition ◽  
Dirac Equation ◽  
Bound States ◽  
Wave Functions ◽  
Expectation Values ◽  
Original Boundary ◽  
Mit Bag Model ◽  
Slight Extension ◽  
Spherical Basis ◽  
Coulomb Potentials

The paper considers the free spherical Dirac equation with a boundary condition at r = R which is a slight extension of the original boundary condition of the MIT bag model. We discuss the basis states and apply them for a diagonalization of Coulomb potentials. The obtained results agree quite well with the lowest bound states with κ = -1, +1 and -2 and their expectation values [Formula: see text]. There appear basis states with energies -mc2 < E < mc2 under certain circumstances of the boundary condition. These states are concentrated at the boundary.

scholarly journals Bosonization of Quantum Sine–Gordon Field with Boundary

1997 ◽  
Vol 12 (09) ◽  
pp. 1711-1741 ◽  
Author(s):  
Bo-Yu Hou ◽  
Kang-Jie Shi ◽  
Yan-Shen Wang ◽  
Wen-Li Yang
Keyword(s):  
Boundary Condition ◽  
Ground States ◽  
Form Factors ◽  
Fixed Boundary ◽  
Boundary Operators ◽  
Sine Gordon Model ◽  
Fixed Boundary Condition

Boundary operators and boundary ground states in sine–Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators. We also obtain the form-factors of this model.

The use of Gaussian (exponential quadratic) wave functions in molecular problems. II. Wave functions for the ground states of the hydrogen atom and of the hydrogen molecule

1960 ◽  
Vol 258 (1294) ◽  
pp. 421-430 ◽  
Keyword(s):  
Hydrogen Atom ◽  
Quadratic Form ◽  
Hydrogen Molecule ◽  
Ground States ◽  
Cylindrical Symmetry ◽  
Binding Energies ◽  
Wave Functions ◽  
Electronic Wave ◽  
Electronic Wave Functions ◽  
Independent Parameters

The results reported in this paper constitute a first examination of the use of Gaussian wave functions with correlation as approximations to electronic wave functions. Functions of the form Σ k = n k =1 C k exp ( – Q k ), where C k is a constant and Q k is a quadratic form corresponding to orbitals with cylindrical symmetry, variable centres and with correlation, are used for the hydrogen molecule. Binding energies of 4∙30, 4∙42, 4∙52 and 4∙58 eV are obtained with functions containing, respectively, 26, 35, 53 and 71 independent parameters. The accuracy of the results and the moderate computing times suggest that there is considerable scope for wave functions of this type. For the hydrogen atom, approximations to the 1 s -orbital in terms of Σ k = n k =1 C k exp ( – a k r 2 ) are given for n = 3, 4, 5, 6 and 8.

scholarly journals Algebraic approach to non-separable two-dimensional Schrödinger equation: Ground states for polynomial and Morse-like potentials

Open Physics ◽  
2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Vladimír Tichý ◽  
Lubomír Skála ◽  
René Hudec
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground States ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Two Dimensional ◽  
One Dimensional

AbstractThis paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrödinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed. Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method.

scholarly journals WKB WAVE FUNCTIONS WITH THE INDUCED GRAVITY THEORY

1999 ◽  
Vol 14 (31) ◽  
pp. 2179-2185 ◽  
Author(s):  
ZONG-HONG ZHU ◽  
LI CAO
Keyword(s):  
Boundary Condition ◽  
Wave Functions ◽  
Gravity Theory ◽  
Wkb Method ◽  
Induced Gravity ◽  
Maximum Value ◽  
Gravitational And Cosmological Constants ◽  
Classical Models ◽  
Cosmological Constants ◽  
The Universe

The Wheeler–DeWitt equation for the induced gravity theory is constructed in the mini superspace approximation, and then solved using the WKB method under three types of boundary condition proposed respectively by Hartle & Hawking ("no boundary"), Linde and Vilenkin ("tunneling from nothing"). It is found that no matter how the gravitational and cosmological "constants" vary in the classical models, they will acquire constant values when the universe comes from quantum creation, and that, in particular, the resulting tunneling wave function under the Linde or Vilenkin boundary condition reaches its maximum value if the cosmological constant vanishes.

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