Background potential

Electrical forerunners may be found out as the result of electrical field potential between two points (electrotelluric field on the earth surface) measurement. Usually the background potential is 10 mV and during the earthquake it equals to 70 mV. 

Quantum Free-Electron Theory Constant-Potential Model, The simple quantum free-electron theory (1) is based on the electron-in-a-box model, where the box is the size of the crystal. This model assumes that (1) the positively charged ions and all other electrons (nonvalence electrons) are smeared out to give a constant background potential (a potential box having a constant interior potential), and (2) the electron cannot escape from the box boundary conditions are such that the wavefunction if/ is... 

Figure 3.6. Plot of energy E versus wavenumber k (a) for a free electron moving in a constant background potential and (b) for an electron moving in a periodic field in an one-dimensional crystal, (c) The energy bands for (b).

Mayer, M. S., Mankin, R. W. and Lemire, G.F. (1984). Quantitation of the insect electro-antennogram measurement of sensillar contributions, elimination of background potentials and relationship to olfactory sensation. Journal of Insect Physiology 30 757-763. 

Table 11.2 Background Potential Limits in Various Nonaqueous Solvents...

Four recent attempts to calculate one-electron energies in UF6 by Xa relativistic techniques70,147-1491 provide a conspicuous dispersion of results in Table 3, much like the comparable quantities calculated for UOj2 in Table 1. At least, the neutral molecule UF6 has no problem needing a background potential. 

Lynd, L. R., Jin, H., Michels, J. G., Wyman, C. E., and Dale, B., Bioenergy Background, Potential, and Policy A policy briefing prepared for the Center for Strategic and International Studies Center for Strategic and International Studies Washington, DC, 2003. 

Figure 11.14 Equations for the differential chemical diffusion coefficient of electronic capacitance for a perm-selective polymeric film species D° is the self-diffusion coefficient. The (a) and for a film with the excess of background potential dependences ofCjif, D, and <7 obtained electrolyte in its bulk (b). In the latter case, the with the useof Equations 11.20-11.22, assuming chemical diffusion coefficient and electronic g= —2) are shown in panel c.

For the ground state, nx — ny — nz —. The mass m is the mass of the valence-shell electron, which is the particle. The rest of the atom simply creates a background potential, Uq, constant in the box. 

Within the jellium model for metal clusters [95,53] as described in the introduction, the positive background potential is in a first approximation normally chosen as a spherical shape of the following form... 

FIG. 20. The periodically varying contribution to the calculated binding energy of spherical sodium cluster. The periodic variations are due to the quantized motion of the electrons in the background potential [71,153]. 

Two methods can be employed to estimate the selectivity ratio based on this curve. The first is based on finding graphically the point at which the electrode is responding equally to both ions. This corresponds to the activity of A from the extrapolated linear portion of the cu ye at which the potential is equal to the background potential due to B (this is the concentration of A that would give that potential if there were no B present, that is, if the curve follows the Nemst equation for A). 

It should be noted that the projection operator A+ and, consequently, the no-pair Hamiltonian depends on the background potential U. One finds however that energies obtained from the no-pair Hamiltonian are only weakly dependent on the potential and that small differences between calculations starting from different potentials can be accounted for in terms of omitted negative-energy corrections. We elaborate on this point in Sec. 4. 

If we choose the background potential to be the Hartrce-Fock potential, U = Fhf, then we find that the energy through first-order is... 

The rules of perturbation theory associated with the relativistic no-pair Hamiltonian are identical to the well-known rules of nonrelativistic many-body perturbation theory, except for the restriction to positive-energy states. The nonrelativistic rules are explained in great detail, for example, in Lindgren and Morrison [30]. Let us start with a closed-shell system such as helium or beryllium in its ground state, and choose the background potential to be the Hartree-Fock potential. Expanding the energy in powers of V) as... 

Note that Eqs. (187) and (188) are derived with the background potential U set to zero and sums over intermediate states and include unoccupied as well as occupied states. Limiting these sums to unoccupied states and n+ leads to an additional term J (VHF)am+(VHF)m+a/( a — iu Eq. (189) from the remaining sums over occupied states in Ei, but the same term will also show up from the electron-electron pair term in Epirao instead of to VkP The bottom line is that the... 

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