Electron stationary

Wigner s formula is open to criticism also on another point, since he assumes the existence of a stationary electron state where the density is so low that the kinetic energy may be neglected. This is in contradiction to the virial theorem (Eq. 11.15), which tells us that the kinetic energy can never be neglected in comparison to the potential energy and that the latter quantity is compensated by the former to fifty per cent. A reexamination of the low density case would hence definitely be a problem of essential interest. 

By convention, a free stationary electron has zero energy, so bound electrons have negative energies. 

Attempts to perform the MAED of these crystallites were unsuccessful because of the difficulty In observing the crystallites with the small objective apertures necessary to obtain reasonable MAED patterns, and the rapid mobility of these small crystallites In the stationary electron beam used In the MAED mode. Instrumental modifications are commercially available which might allow this measurement to be made. 

In the joint presence of an electric field E and a magnetic field B in a medium, the stationary electron velocity can be written as... 

It follows that the wave function for nuclear motion is calculated in an effective potential E (Q) obtained from the energy eigenvalues of the stationary electronic state. 

In a line of reasoning that many of the younger quantum physicists regarded as reactionary, Schrodinger built his treatment of the electron on the well-understood mathematical techniques of wave equations as partial differential equations involving second derivatives. Schrodinger s equation for stationary electron states, as written in the Annalen der Physik in 1926, took the form... 

Here we benefit from the notion of stationary electron density. The particles are not at rest, but the probability density does not change with time. 

Fig. 2.4 The scattering of a photon by a stationary electron in the Compton effect.

This uncertainty is an inescapable fact of the world we live in, which is illustrated beautifully by the following gedanken experiment suggested by Bohr. Suppose we wish to measure the position of a stationary electron using a microscope as shown in Fig. 2.6. Then from optics the resolution of the microscope will be given by... 

In the last section it was shown that instead of representing an electrode potential on a relative scale (arbitrarily setting the standard hydrogen electrode potential equal to zero), it is possible to numerically calculate the actual value of the latter, with a reference state of zero energy for the stationary electron at infinity in a vacuum. 

Figure 2.4 In Compton scattering a photon of energy hv and velocity c hits a stationary electron e the outgoing (scattered) photon at an angle 6 keeps this velocity but has a different energy hv while the electron acquires a velocity v...

The quantum theory of molecular structure developed here and the standard BO approach rely on the separability between electronic and nuclear configurational degrees of freedom. However, the way this is achieved differs radically between the approaches. In the treatment described here, the nuclei are seen to be trapped by an attractor generated by the stationary electronic wave function (nuclei follow the electronic states ) the electronic wave function does not depend upon the instantaneous positions of the nuclei as early proposed by this author [4] a change of electronic state, characterizing a chemical reaction with reactants and products in their ground electronic states, is described as a Franck-Condon like process. 

Let us assume then the existence of a stationary electronic state H(p) transforming according to one ofthe irreducible representations ofthe symmetry group to which it belongs. We contend that this wave function determines a stationary... 

The reference frame depends upon the stationary electronic state (if any) derived from a diagonalization ofthe electronic hamiltonian He (T ). 

For non-stationary processes the motion of the center of mass produced by external sources (sound waves for instance) can be coupled to the electro-nuclear system via its total momentum operator p (cf. eq.(9)). Not only vibrational excitations but also electronic ones can be mediated by non-stationary motion of the center of mass. This is a feature related to the stationary frame determined by a particular stationary electronic state. 

The theory discussed here gives a special role to the stationary states of the molecular hamiltonian. In particular, there are stationary electronic states, not a set of electrons. For example, the hydrogen atom cannot be seen as formed by one proton plus one electron. It is the electronic spectra which define it, not the model we use to calculate the energy levels and wave functions. This may sound strange but consider a thermal neutron. This system decomposes into one proton plus an electron and a neutrino. One cannot say that a neutron is made of such particles. Matter may exist in different kinds of stationary states processes can be seen as changes among them. 

Inasmuch as a and ji bonds can be treated more or less independently [5,6], the non-stationary electronic states before and after electron transfer can be expressed in terms of two Heitler-London covalently bonded tt-electrons... 

If the amount of mass transferred is analyzed, further conclusions on the carrier type (ionic/electronic) can be drawn according to Faraday s law, simply because of the fact that the pure stationary electronic flux will not cause mass displacements. If also the direction of mass transport is analyzed, e.g., by recording the position variation of the boundaries, cationic and anionic conductivities may be distinguished (Tubandt-Hittorf experiments). 

For a given set of nuclear coordinates R and a stationary electronic wavefunction CFel) normalised to 1 (i.e., (vPel f el) = 1 holds true), the electronic energy can be calculated in the Bom-Oppenheimer approximation as the expectation value of the electronic Hamiltonian operator as follows ... 

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