About the world described by Quantum Chemistry

S. FORTIN; J. A. JAIMES ARRIAGA; H. ACCORINTI

Praga

Congreso; International Congress of Logic, Methodology and Philosophy of Science and Technology 2019 (CLMPST 2019); 2019

International Union of History and Philosophy of Science and Technology

One of the oldest problems associated with the interpretation of Quantum Mechanics is the role of the wave function in the ontology of the theory. Although Schrodinger himself posed the problem from the beginning of the theory, even today the meaning of the wave function remains the subject of debate. In this context, the problem of the 3N dimensions of the wave function is of particular interest in the philosophy of physics. As the wave function associated with a system of N particles is written in a space of 3N dimensions, it is necessary to ask about the meaning of this space. The debates around the issue have an important impact on the way in which we conceive the world around us. This is clearly manifested by the intense discussions that have taken place in recent years (Albert 2013, Allori 2013, Monton 2006). In this work we will introduce a new perspective, coming from the way in which the wave function is used in scientific practice. Our objective is to investigate the ontology of quantum chemistry emerging from the analysis of the use of the wave function when quantum mechanics is applied to specific cases in the chemical domain. In the field of quantum chemistry there was not much discussion about the meaning of the wave function, and for this reason we consider that it can offer a fruitful context for a philosophical analysis. The typical many body system in this context is a molecule, and the typical problem is to find the energy spectrum of an electron that is in interaction with many other particles. To find such a spectrum, the so called orbital approximation is usually appealed to, which makes it possible to write the total wave function of the system as a product of mono-electron wave functions (Atkins & de Paula 2006). Under this approximation, the wave function of a given electron depends only on the variables of this electron; therefore, it evolves in the space of three dimensions (Lowe & Peterson 2006). In this presentation we will show that the procedure performed by chemists when they use the orbital approximation can be formalized as the result of the application of two mathematical operations: first, a projection onto a subspace of the Hilbert space, and second, a change of variables. With the help of this formalization, we will go beyond the approximation itself and propose an ontology specific to quantum chemistry.