Slow-moving electrons

The problems for quantum chemists in the mid-forties were how to improve the methods of describing the electronic structure of molecules, valence theory, properties of the low excited states of small molecules, particularly aromatic hydrocarbons, and the theory of reactions. It seemed that the physics needed was by then all to hand. Quantum mechanics had been applied by Heitler, London, Slater and Pauling, and by Hund, Mulliken and Hiickei and others to the electronic structure of molecules, and there was a good basis in statistical mechanics. Although quantum electrodynamics had not yet been developed in a form convenient for treating the interaction of radiation with slow moving electrons in molecules, there were semi-classical methods that were adequate in many cases. 

In general, a positive ion and two slow moving electrons result. The probability of the process increases nearly linearly with the kinetic energy of the impacting electron up to a maximum (at around 100-200 eV). After this maximum the probability decreases slowly. 

Let us consider a slow-moving electron, i.e. the magnitude of the linear momentum p is negligible compared to m0c. Then the eigenvalues of the Dirac equation are dominated by E0 hence... 

All the derivations made up to now have been rigorous. We are interested in comparing the relativistic and the non-relativistic Hamiltonian terms, which can be done approximately in the following way. The Dirac Hamiltonian is assumed in the form of the dominating term for the positive energy solutions E0 and the small perturbation HNR due to a slow-moving electron... 

The path integral formulation of quantum theory provides a framework to describe the behavior of solvated electrons. Feynman used the approach to treat the slow moving electron in ionic crystals — the prototypical polaron problem. We have extended this theory, drawing on theories of the liquid state, to analyze the localization transition and related phenomena found with excess electrons in fluids. 

By examining through simulation the structures of the isomorphic polymers, researchers gain a geometrical perspective of electronic states in a liquid environment. It is a perspective that Feynman usefully exploited long ago in his treatment of the slow moving electron in an... 

We assume that the nuclei are so slow moving relative to electrons that we may regard them as fixed masses. This amounts to separation of the Schroedinger equation into two parts, one for nuclei and one for electrons. We then drop the nuclear kinetic energy operator, but we retain the intemuclear repulsion terms, which we know from the nuclear charges and the intemuclear distances. We retain all terms that involve electrons, including the potential energy terms due to attractive forces between nuclei and electrons and those due to repulsive forces... 

Undei the Born Oppenheinier approximaii.on. the nuclei ai e assumed to be so much more massive and slow moving than the electrons that their motions are independent and can be treated separately. This permits the Hamiltonian in Hq, (9-4) to be separated into tw o parts, one that refers to nuclei only... 

The biflagellate unicellular green alga Chlamydomonas reinhardtii is prone to spontaneous mutations that produce deficiencies in flagellar proteins and MT assembly, substructure, and function. Viable mutants that are either nonmotile or slow moving can be isolated and analyzed biochemically and morphologically, thereby establishing structure-function correlations. Electron microscopic analysis... 

An eventual connection is formed due to the Born-Oppenheimer-Huang (BOH) [3,4] treatment. Within this treatment Born and Oppenheimer distinguished between the fast moving electrons and the slow moving nuclei and presented the total wave function (of the nuclei and the electrons) in the form ... 

Just like the adiabatic framework, expressed in terms of equation (4), the diabatic one which avoids the NACTs altogether follows from the same basic observation, namely, that molecular systems contain fast and slow moving particles. However, instead of applying an electronic basis set which varies with the nuclear coordinates one may employ a single basis set as calculated at one point in configuration space. Following this idea it can be shown that the relevant SE is [19] ... 

Although diffusion is a slow process compared to energy transfer and electron transfer at the shortest distances, it can be an exceptionally effective way to move electrons and protons over long distances. However, unlike the hard-wired cofactor chains that guide electron transfer in protein complexes, diffusion faces the problem of directing where... 

For molecules, a common simplification is the Born-Oppenheimer separation in which the slow-moving nuclei and the fast-moving electrons are treated separately. Using this approximation (and suppressing the q dependence), we first solve the electronic Schrodinger equation ... 

In the pulsed mode of operation, which is usually the preferred mode, a mixture of methane in argon is usually employed as the carrier gas. Pure argon can not be used very effectively as the carrier gas as the diffusion rate of electrons in argon is ten times less than that in a 10% methane-90% argon mixture. The period of the pulsed potential is adjusted such that relatively few of the slow negatively charged molecules reach the anode, but the faster moving electrons are all collected. 

A kinematic region that is extremely difficult for quantum calculations is just above the ionisation threshold. Near threshold the two slow continuum electrons moving in the field of a positive ion are strongly correlated and suitable approximations are difficult to evaluate. The main features in the asymptotic region were first established theoretically by... 

A metallic conductor is a substance that has a partially filled band. It takes very little energy to move electrons from a filled level to an empty level in a band this results in high conductivity because there is no energy gap at the Fermi level. When the temperature of a metallic conductor is lowered, the conductivity increases because the thermal motion of the atoms in the crystal is slowed, allowing the electrons to move more easily. 

While electrons are now commonly said to be both particles and waves or neither people live in a macroscopic, slow-moving world and lack the ability to truly imagine a particle-wave. This difficulty was nicely stated by Jacob Bronowski On Mondays, Wednesdays and Fridays, the electron would behave like a particle on Tuesdays, Thursdays and Saturdays it would behave as a wave. ... 

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