The variational cellular method for quantum mechanical applications: Calculations of the ground and excited states of F2 and Ne2 molecules

2009 ◽  
Vol 20 (S15) ◽  
pp. 401-408
Author(s):  
José R. Leite ◽  
Adalberto Fazzio ◽  
Marco A. P. Lima ◽  
A. M. Dias ◽  
Abel Rosato ◽  
...  
Keyword(s):  
Excited States ◽  
Quantum Mechanical ◽  
Cellular Method

scholarly journals Quantum-mechanical hydration plays critical role in the stability of firefly oxyluciferin isomers: State-of-the-art calculations of the excited states

2020 ◽  
Vol 153 (20) ◽  
pp. 201103
Author(s):  
Yoshifumi Noguchi ◽  
Miyabi Hiyama ◽  
Motoyuki Shiga ◽  
Hidefumi Akiyama ◽  
Osamu Sugino
Keyword(s):  
Excited States ◽  
State Of The Art ◽  
Critical Role ◽  
Quantum Mechanical ◽  
The Stability

scholarly journals Application of the quantum mechanical hypervirial theorems to even-power series potentials

2020 ◽  
Vol 5 ◽  
pp. 104
Author(s):  
T. E. Liolios ◽  
M. E. Grypeos
Keyword(s):  
Power Series ◽  
Excited States ◽  
Energy Operator ◽  
Quantum Mechanical ◽  
Expectation Values ◽  
Gaussian Potential ◽  
Energy Eigenvalues ◽  
The Mean ◽  
Potential Parameters ◽  
Feynman Theorem

The class of the even-power series potentials:V(r)=-D+ Σ_k^{\infty} V_kλ^kr^{2k+2}, Vo=ω^2>0, is studied with the aim of obtaining approximate analytic ex­pressions for the energy eigenvalues, the expectation values for the potential and the kinetic energy operator, and the mean square radii of the orbits of a particle in its ground and excited states. We use the Hypervirial Theorems (HVT) in conjunction with the Hellmann-Feynman Theorem (HFT) which provide a very powerful scheme especially for the treatment of that type of potentials, as previous studies have shown. The formalism is reviewed and the expressions of the above mentioned quantities are subsequently given in a convenient way in terms of the potential parameters and the mass of the particle, and are then applied to the case of the Gaussian potential and to the potential V(r)=-D/cosh^2(r/R). These expressions are given in the form of series expansions, the first terms of which yield in quite a number of cases values of very satisfactory accuracy.

ChemInform Abstract: Linear-Scaling Quantum Mechanical Methods for Excited States

ChemInform ◽  
2012 ◽  
Vol 43 (31) ◽  
pp. no-no
Author(s):  
ChiYung Yam ◽  
Qing Zhang ◽  
Fan Wang ◽  
GuanHua Chen
Keyword(s):  
Excited States ◽  
Quantum Mechanical ◽  
Linear Scaling ◽  
Mechanical Methods

scholarly journals e+e− Annihilation in Strong Magnetic Fields

1981 ◽  
Vol 95 ◽  
pp. 35-36
Author(s):  
G. Wunner ◽  
H. Herold ◽  
H. Ruder
Keyword(s):  
Magnetic Fields ◽  
Excited States ◽  
Quantum Mechanical ◽  
Annihilation Process ◽  
Strong Magnetic Fields ◽  
Two Body Problem ◽  
Quantum Mechanical Treatment ◽  
Electron Positron ◽  
Correct Quantum ◽  
Free Case

The possible existence of electron-positron plasmas in the magnetosphere of neutron stars gives rise to the question in which way the e+e− annihilation process is modified by the strong magnetic fields prevailing there. On the basis of a correct quantum mechanical treatment of the two-body problem in an external magnetic field we have calculated lifetimes of the ground state as well as of excited states of bound e+e− pairs (positronium). We find that the 1γ decay remains strictly forbidden, whereas the 2γ process is strongly enhanced with respect to the field-free case.

scholarly journals On the modification of methods of nuclear chronometry in astrophysics and geophysics

Open Physics ◽  
2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Vladislav Olkhovsky ◽  
Marina Dolinska
Keyword(s):  
Excited States ◽  
Cosmic Radiation ◽  
Quantum Mechanical ◽  
Α Decay ◽  
Upper Limits ◽  
Mechanical Approach ◽  
Nuclear Synthesis ◽  
Quantum Mechanical Approach ◽  
Α Particles

AbstractIn practically all known methods of nuclear chronometry until now, research has usually taken into account the life-times of only the fundamental states of α-radioactive nuclei. But in the processes of nuclear synthesis in stars and under the influence of constant cosmic radiation on the surfaces of planets the excitations of the α-radioactive nuclei are still ongoing. Between these processes there are states with excited α-particles inside the parent nuclei leading to much smaller life-times. And inside the large masses of stellar, terrestrial and meteoric substances there are transitions between different internal conditions of radioactive nuclei that are accompanied by infinite chains of γ-radiations with subsequent γ-absorptions, further γ-radiations, etc. For a description of the α-decay evolution that accounts for such excited states and multiple γ-radiations and γ-absorptions inside stars, and under the influence of cosmic radiation on the Earth’s surface we present a quantum-mechanical approach, which is based on the generalized Krylov-Fock theorem. A few simple estimations are also presented. These approaches lead to the conclusion that the usual (non-corrected) “nuclear clocks” do really point not to realistic values but to the upper limits of the durations of α-decay in stellar and planet processes.

Compression effects on dipole transitions and state lifetimes for a hydrogen atom

2016 ◽  
Vol 94 (9) ◽  
pp. 894-901 ◽  
Author(s):  
A. Solórzano ◽  
N. Aquino ◽  
A. Flores-Riveros
Keyword(s):  
Boundary Condition ◽  
Hydrogen Atom ◽  
Excited States ◽  
Dirichlet Boundary ◽  
Numerical Technique ◽  
Oscillator Strengths ◽  
Quantum Mechanical ◽  
Mechanical Problem ◽  
Radial Schrödinger Equation ◽  
Compression Effects

The quantum mechanical problem of a hydrogen atom placed at the center of an impenetrable sphere of radius r0 is solved by using two different methods, where, in the first, a trial wave function, consisting of a hydrogen-like function times a cutoff factor that ensures fulfillment of Dirichlet boundary condition, is proposed, whereas in the second, the radial Schrödinger equation is solved by means of an accurate numerical technique. We computed the energies for the ground and first excited states of S-, P-, and D-symmetry, as well as dipole transitions, oscillator strengths, and a few state lifetimes. Although the variational method and the numerical solution are found to give similar qualitative behaviours, which, in general, compare reasonably well with some results published previously, the 2p state lifetimes obtained in the present calculations appear to be at variance with the latter at some particular box radii.

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