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Quantum Physics for Scientists and Technologists: Fundamental Principles and Applications for Biologists, Chemists, Computer Scientists, and Nanotechnologists by Paul Sanghera

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5

PRINCIPLES AND FORMALISM OF QUANTUM MECHANICS

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

David Hilbert

Figure 5.0. Portrait of a Philosopher, 1915.

Courtesy of Lyubov Popova. From Petrova, bassner, Burliuk-Holt, Russian Futurism.

Formalism is a process to capture the truth in a given field in terms of a set of rules without dealing with any truth that may exist outside the framework of these rules. Therefore, formalism lends itself well to disciplines that are based upon axiomatic systems, where an axiom, also called a postulate, is a proposition that is not proved or demonstrated, but is generally considered to be either self-evident or true. The word “axiom” comes from the Greek word, which means “to deem worthy”. For example, from the viewpoint of a formalist, mathematics is no more than symbols with certain meanings, connected according to some logic and a few elementary rules. The truth of the postulate is taken for granted, and serves as a starting point for deducing and inferring other truths, which in science we call theoretical predictions. This is where the postulates are put to the test by testing the predictions with experiments. However, be warned that outside the fields of logic and mathematics, the term “axiom” is sometimes used loosely for any established principle of a field.In this chapter, you will venture through the formalism of quantum mechanics.

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