Date
5-15-2015
Document Type
Thesis
Abstract
In this thesis we explore the mathematical foundations that unite physics at a quantum scale, quantum mechanics, with a macroscopic scale, classical mechanics. We seek to understand the mathematical motivation behind the quantum-classical correspondence and how it unites two seemingly different theories of the physical world. We show how this correspondence binds the Hamiltonian theory of classical physics to the Hilbert space theory in quantum mechanics, and establish a way to translate between classical observables and quantum operators, using the Fourier transform. These approaches to “quantizing” a physical state can be applied generally to a wide variety of observable quantities in classical mechanics.
Department
Mathematics
Thesis Comittee
Matt Salomone (thesis supervisor)
Copyright and Permissions
Original document was submitted as an Honors Program requirement. Copyright is held by the author.
Recommended Citation
Culver, Nina. (2015). A Mathematical Foundation of the Quantum-Classical Correspondence. In BSU Honors Program Theses and Projects. Item 82. Available at: https://vc.bridgew.edu/honors_proj/82
Copyright © 2015 Nina Culver