Schrodinger’s model

The modern concept of the atom corresponds to Schrodinger s model. 

Schrodinger s model of the atom is a mathematical formulation of quantum mechanics that describes the electron density of orbitals. It is the atomic model that has been in use from shortly after it was introduced up to the pr<, ... 

The imprecise nature of Schrodinger s model was supported shortly afterwards by a principle proposed by Werner Heisenberg, in 1927. Heisenberg demonstrated that it is impossible to know both an electron s pathway and its exact location. Heisenberg s uncertainty principle is a mathematical relationship that shows that you can never know both the position and the momentum of an object beyond a certain measure of precision. 

Access to most of Schrodinger s modelling and cheminformatics tools... 

Describe the major similarities and differences between Schrodinger s model of the atom and the model proposed by Bohr. 

The coming of wave mechanics, which should have been hailed as final vindication of the proposed wave nature of electrons, already surmised and soon to be demonstrated experimentally at the time, was successfully resisted as inadequate to account for cloud-chamber trajectories and the Compton effect. Although both objections are spurious, they had such authority in support that an illogical watered-down reinterpretation of Schrodinger s model gained universal acceptance. The consequences for theoretical chemistry have been disastrous. 

In recent years the old quantum theory, associated principally with the names of Bohr and Sommerfeld, encountered a large number of difficulties, all of which vanished before the new quantum mechanics of Heisenberg. Because of its abstruse and difficultly interpretable mathematical foundation, Heisenberg s quantum mechanics cannot be easily applied to the relatively complicated problems of the structures and properties of many-electron atoms and of molecules in particular is this true for chemical problems, which usually do not permit simple dynamical formulation in terms of nuclei and electrons, but instead require to be treated with the aid of atomic and molecular models. Accordingly, it is especially gratifying that Schrodinger s interpretation of his wave mechanics3 provides a simple and satisfactory atomic model, more closely related to the chemist s atom than to that of the old quantum theory. 

Schrodinger s equation is widely known as a wave equation and the quantum formalism developed on the basis thereof is called wave mechanics. This terminology reflects historical developments in the theory of matter following various conjectures and experimental demonstration that matter and radiation alike, both exhibit wave-like and particle-like behaviour under appropriate conditions. The synthesis of quantum theory and a wave model was first achieved by De Broglie. By analogy with the dual character of light as revealed by the photoelectric effect and the incoherent Compton scattering... 

The essence of Schrodinger s treatment was to replace the classical orbit of Bohr s semi-classical (particle) model of the H-atom by a corresponding wavelike orbital (single-electron wavefunction) L. Instead of specifying the electron s... 

Nevertheless, very-long-lived quasi-stationary-state solutions of Schrodinger s equation can be found for each of the chemical structures shown in (5.6a)-(5.6d). These are virtually stationary on the time scale of chemical experiments, and are therefore in better correspondence with laboratory samples than are the true stationary eigenstates of H.21 Each quasi-stationary solution corresponds (to an excellent approximation) to a distinct minimum on the Born-Oppenheimer potential-energy surface. In turn, each quasi-stationary solution can be used to construct an alternative model unperturbed Hamiltonian //(0) and perturbative interaction L("U),... 

There are some scientists and philosophers who still claim that a model by definition "furnishes a concrete image" and "does not constitute a theory." 10 But if the model is the mathematical description, then the question of whether the model is the theory appears to become moot, since most people accept the view that rigorous mathematical deduction constitutes theory. For others, like Hesse and Kuhn, even if the model is a concrete image leading to the mathematical description, it still has explanatory or theoretical meaning, for, as Kuhn put it, "it is to Bohr s model, not to nature, that the various terms of the Schrodinger equation refer." 11 Indeed, as is especially clear from a consideration of mathematical models in social science, where social forces are modeled by functional relations or sets of mathematical entities, the mathematical model turns out to be so much simpler than the original that one immediately sees the gap between a "best theory" and the "real world." 12... 

The explanatory system which dramatically combined the classification methods of natural history with the quantitative methods of physical laws was the periodic system worked out by Dmitri Mendeleev (and independently, although less successfully, by Meyer). What is the great tableau that is the periodic table Is it icon, index, or symbol It is not metaphor. Is it a model There is no chemical laboratory in the world where Mendeleev s table does not hang on the wall, despite the fact that the original version is well over one hundred years old. Its center remains untouched. Give a chemist a choice between the periodic table (fig. 4) and Schrodinger s equation. Which would she take ... 

It is then quite understandable why, without the necessary mathematical machinery, the relevant concepts cannot be properly grasped. On the other hand, the mathematical disguise that is characteristic of quantum-chemistry courses makes both teachers and students pay more attention to the complexities of the mathematics (the tools, the trees ) and lose the physics (the actual world, the forest ). Although mathematics is essential for a deep understanding of quantum chemistry, the underlying physical picture and its connection with mathematics are equally important. AOs, MOs and related concepts derive from SchrOdinger s wave mechanics, which is an approximation to nature. According to Simons (96), "orbital concepts are merely aspects of the best presently available model they are not real in the same sense that experimental observations are. ... 

Schrodinger s quantum mechanical model of atomic structure is framed in the form of a wave equation, a mathematical equation similar in form to that used to describe the motion of ordinary waves in fluids. The solutions (there are many) to the wave equation are called wave functions, or orbitals, and are represented by... 

This is physically implausible, as no finite force can make die potential change suddenly, certainly not from zero to infinity It is, however, a useful model, known as the particle in a box, which illustrates some important features of Schrodinger s equation. 

Soon after first publication Schrodinger s wave-mechanical model was extended by Madelung [39] on the basis of the obvious correspondence with the classical theory of hydrodynamics, already pointed out in Schrodinger s original papers [34] (II,p.l7). Writing the time dependence of k in terms of an action function... 

Electronic transition between stationary states consists in the transfer of a photon by the Wheeler-Feynmann handshake mechanism which implies the photon to exist between the radial surfaces of the two vibrating states before emission or absorption, exactly as envisaged in Schrodinger s beat model for electron transition. 

It is interesting to note that the Gottingen school, who later developed matrix mechanics, followed the mathematical route, while Schrodinger linked his wave mechanics to a physical picture. Despite their mathematical equivalence as Sturm-Liouville problems, the two approaches have never been reconciled. It will be argued that Schrodinger s physical model had no room for classical particles, as later assumed in the Copenhagen interpretation of quantum mechanics. Rather than contemplate the wave alternative the Copenhagen orthodoxy preferred to disperse their point particles in a probability density and to dress up their interpretation with the uncertainty principle and a quantum measurement problem to avoid any wave structure. 

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