scholarly journals The Hellmann-Feynman Theorem Revisited.

2020 ◽  
Author(s):  
Joshua Rackers
Keyword(s):  
Feynman Theorem

Generalisation of the Hellmann-Feynman theorem to Gamow states

1987 ◽  
Vol 20 (10) ◽  
pp. 2859-2864 ◽  
Author(s):  
P Ziesche ◽  
K Kunze ◽  
B Milek
Keyword(s):  
Gamow States ◽  
Feynman Theorem

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.

scholarly journals The Hellmann–Feynman theorem at finite temperature

2020 ◽  
Vol 88 (6) ◽  
pp. 503-510
Author(s):  
Marina Pons ◽  
Bruno Juliá-Díaz ◽  
Artur Polls ◽  
Arnau Rios ◽  
Isaac Vidaña
Keyword(s):  
Finite Temperature ◽  
Feynman Theorem

scholarly journals On the Hellmann-Feynman theorem in statistical mechanics

2020 ◽  
Vol 384 (22) ◽  
pp. 126531
Author(s):  
Paolo Amore ◽  
Francisco M. Fernández
Keyword(s):  
Statistical Mechanics ◽  
Feynman Theorem

scholarly journals A Deduction of the Hellmann-Feynman Theorem

2020 ◽  
Vol 59 (5) ◽  
pp. 1396-1401 ◽  
Author(s):  
Chen Feng ◽  
Cheng Wei ◽  
Bao-long Fang ◽  
Hong-yi Fan
Keyword(s):  
Feynman Theorem

Generalized Hellmann-Feynman Theorem for Coupled Anisotropic Two-Mode Boson System

2010 ◽  
Vol 49 (6) ◽  
pp. 1200-1211 ◽  
Author(s):  
Xue-Xiang Xu ◽  
Li-Yun Hu ◽  
Hong-Chun Yuan
Keyword(s):  
Boson System ◽  
Feynman Theorem

Exact formula for the dipole moment of a one-electron diatomic molecule

1985 ◽  
Vol 401 (1821) ◽  
pp. 373-392 ◽  
Keyword(s):  
Dipole Moment ◽  
Electronic State ◽  
Diatomic Molecule ◽  
Recursion Relation ◽  
Energy Eigenvalue ◽  
Exact Formula ◽  
Electronic Energy ◽  
Moment Function ◽  
Expectation Values ◽  
Feynman Theorem

It is shown that the dipole moment function, μ ( R , Z a , Z b ), for an arbitrary bound electronic state of a one-electron diatomic molecule, with inter-nuclear distance R and atomic numbers Z a , Z b may be expressed exactly in terms of the separation eigenconstant C and the electronic energy eigenvalue W of the Schrödinger equation by means of the Hellmann-Feynman theorem and a new recursion relation. The formula is used to investigate the behaviour of μ in the vicinity of the united atom and when the nuclei are far apart. The generalization required to extend the relation to other expectation values is derived in an appendix.

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