# Dirac, Von Neumann, and the Derivation of the Quantum Formalism

# Dirac, Von Neumann, and the Derivation of the Quantum Formalism

State Vectors in Hilbert Space

The evolution of quantum mechanics through the 1920s was profoundly messy. Some physicists believed that it was necessary to throw out much of the conceptual baggage that early quantum mechanics tended to carry around with it and re-establish the theory on much firmer ground. It was at this critical stage that the search for deeper insights into the underlying reality was set aside in favour of mathematical expediency. All the conceptual problems appeared to be coming from the wavefunctions. But whatever was to replace them needed to retain all the properties and relationships that had so far been discovered. Dirac and von Neumann chose to derive a new quantum formalism by replacing the wavefunctions with *state vectors* operating in an abstract *Hilbert space*, and formally embedding all the most important definitions and relations within a system of axioms.

*Keywords:*
Paul Dirac, John von Neumann, state vectors, Hilbert space, quantum formalism, axioms, classical unit vectors, Hamiltonian operator, time evolution operator

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .