Schrodinger wave mechanics

Wave mechanics (Schrodinger) or quantum mechanics (Heisenberg)... 

In his first communication23 on the new wave mechanics, Schrodinger presented and solved his famous Eq. (1.1) for the one-electron hydrogen atom. To this day the H atom is the only atomic or molecular species for which exact solutions of Schrodinger s equation are known. Hence, these hydrogenic solutions strongly guide the search for accurate solutions of many-electron systems. 

The occurrence of discrete energy states of a bound electron in an atom and the co-existence of wave and particle properties in a free electron, can be accounted for on the basis of wave mechanics (Schrodinger, 1926). Observation of the diffraction patterns produced when electrons of known energy encounter crystals of known atomic spacing shows that the wave length, A, associated with an electron of velocity, v, is given by... 

Eigen function In wave mechanics, the Schrodinger equation may be written using the Hamiltonian operator H as... 

Schrodinger wave equation The fundamental equation of wave mechanics which relates energy to field. The equation which gives the most probable positions of any particle, when it is behaving in a wave form, in terms of the field. 

E. Schrodinger, Ann. Phys. 81, 109 (1926), English translation appears in Collected Papers in Wave Mechanics, E, Schrodinger, ed., Blackie and Sons, London, 1928, p. 102. 

Only with Bohr s 1913-1923 introduction of the "old quantum theory" (itself strongly inspired by chemical periodicity patterns vide infra) and the final discovery of Schrodinger s wave mechanics in 1925 would the periodic table be supplanted as the deepest expression of current chemical understanding ([21], p 2). 

In Schrodinger s wave mechanics (which has been shown4 to be mathematically identical with Heisenberg s quantum mechanics), a conservative Newtonian dynamical system is represented by a wave function or amplitude function [/, which satisfies the partial differential equation... 

Stark effect of a hydrogen-like atom, using the Schrodinger wave mechanics. Their equation, obtained independently and by different methods, is... 

Wave mechanics is based on the fundamental principle that electrons behave as waves (e.g., they can be diffracted) and that consequently a wave equation can be written for them, in the same sense that light waves, soimd waves, and so on, can be described by wave equations. The equation that serves as a mathematical model for electrons is known as the Schrodinger equation, which for a one-electron system is... 

When wave mechanical calculations are made according to the Schrodinger equation, the probability of finding the electron in a node is zero, but this treatment ignores relativistic considerations. When such considerations are applied, Dirac has shown that nodes do have a very small electron density Powell, R.E. J. Chem. Educ., 1968,45,558. See also Ellison, F.O. and Hollingsworth, C.A. J. Chem. Educ., 1976, 53, 767 McKelvey, D.R. J. Chem. Educ., 1983, 60, 112 Nelson, P.G. J. Chem. Educ., 1990, 67, 643. For a review of relativistic effects on chemical structures in general, see Pyykko, P. Chem. Rev., 1988, 88, 563. 

Quantum theory was developed during the first half of the twentieth century through the efforts of many scientists. In 1926, E. Schrbdinger inteijected wave mechanics into the array of ideas, equations, explanations, and theories that were prevalent at the time to explain the growing accumulation of observations of quantum phenomena. His theory introduced the wave function and the differential wave equation that it obeys. Schrodinger s wave mechanics is now the backbone of our current conceptional understanding and our mathematical procedures for the study of quantum phenomena. 

Up to this point we have considered particle motion only in the jc-direetion. The generalization of Schrodinger wave mechanics to three dimensions is straightforward. In this section we summarize the basic ideas and equations of wave mechanics as expressed in their three-dimensional form. 

Erwin Schrodinger (1887-1961 Nobel Prize for physics 1932) transferred the concept of wave-particle duality of matter developed by L. V. de Broglie for electrons to the whole atom and thus developed wave mechanics. The Schrodinger equation allows a description of orbitals as the probability of the location of the electrons. Wave mechanics represented a significant development, but were subsequently shown to be insufficient. 

---