Friday, September 13, 2019
12:15pm – 1:15pm

Storrs Campus
GS-119

Prof. P. Mannheim, Department of Physics, University of Connecticut

Quantum mechanics off the beaten track

We discuss some non-conventional options for quantum theory. We show that it is not always possible to write the momentum operator as the familiar derivative operator $$-id/dx$$ where x is real, and discuss what one should then do. We show that basis states do not need to be normalizable to be complete, and even if normalizable do not have to obey the standard Dirac completeness relation $$\sum |n><n| = 1$$. We show that not only do Hamiltonians not need to be Hermitian to have real eigenvalues, they do not even have to be diagonalizable or possess a complete spectrum of energy eigenstates. We discuss how to formulate quantum mechanics in such cases. Following work by Bender and Mannheim [Phys. Rev. Lett. 100, 110402 (2008)] we show how these issues are relevant to the construction of a consistent theory of quantum gravity in four spacetime dimensions.

Contact:

Prof. V. Kharchenko

Physics Department (primary), College of Liberal Arts and Sciences, UConn Master Calendar