Schrodinger formulation

Werner Heisenberg stated that the exact location of an electron could not be determined. All measuring technigues would necessarily remove the electron from its normal environment. This uncertainty principle meant that only a population probability could be determined. Otherwise coincidence was the determining factor. Einstein did not want to accept this consequence ("God does not play dice"). Finally, Erwin Schrodinger formulated the electron wave function to describe this population space or probability density. This equation, particularly through the work of Max Born, led to the so-called "orbitals". These have a completely different appearance to the clear orbits of Bohr. 

Only those problems that can be reduced to one-dimensional one-particle problems can be solved in closed form by the methods of wave mechanics, which excludes all systems of chemical interest. As shown before, several chemical systems can be approximated by one-dimensional model systems, such as a rotating diatomic molecule modelled in terms of a rotating particle in a fixed orbit. The trick is to find a one-dimensional potential function, V that provides an approximate model of the interaction of interest, in the Schrodinger formulation... 

Quantum theory was developed primarily to find an explanation for the stability of atomic matter, specifically the planetary model of the hydrogen atom. In the Schrodinger formulation the correct equation was obtained by recognizing the wave-like properties of an electron. The first derivation by Schrodinger [30] was done by analogy with the relationship that was known to exist between wave optics and geometrical optics in the limit where the index of refraction, n does not change appreciably over distances of order A. This condition leads to the eikonal equation (T3.15)... 

Erwin Schrodinger (1887-1961). Austrian physicist. Schrodinger formulated wave mechanics, which laid the foundation for modern quantum theory. He received the Nobel Prize in Physics in 1933. 

While not unique, the Schrodinger picture of quantum mechanics is the most familiar to chemists principally because it has proven to be the simplest to use in practical calculations. Hence, the remainder of this section will focus on the Schrodinger formulation and its associated wavefunctions, operators and eigenvalues. Moreover, effects associated with the special theory of relativity (which include spin) will be ignored in this subsection. Treatments of alternative formulations of quantum mechanics and discussions of relativistic effects can be found in the reading list that accompanies this chapter. 

However, the wave-particle duality matches perfectly and always with HUR in its standard (Schrodinger) formulation of Eq. (2.99) on the other side, the wave-particle exact equivalence (PAV = 1) may be acquired only in the free evolution regime that, in turn, it is driven by modified HUR as given by Eq. (4.563). In other words, it seems that any experiment or observation upon a quantum object or system would destroy the PAV balance specific for free quantum evolution towards the undulatory manifestation through measurement. 

The state-selective approach to the multi-reference problem was further developed by Banerjee and Simons [118], by Laidig and Bartlett [119], by Hoffmann and Simons [120], by Li and Paldus [121, 122] and by Jeziorski, Paldus and Jankowski [123] who formulated extensive open-shell cc theory, based on the unitary group approach (uga) formalism. The Rayleigh-Schrodinger formulation of a state-selective approach to the multi-reference correlation problem has been developed more recently by Mukherjee and his collaborators [124-130] and also by Schaefer and his colleagues [131-133]. 

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