Physics Commons^™

Building Confidence In The Dirac Δ-Function, Asim Gangopadhyaya, Constantin Rasinariu

Constantin Rasinariu

In this note we present an example from undergraduate quantum mechanics designed to highlight the versatility of the Dirac δ-function. Namely, we compute the expectation value of the Hamiltonian of a free particle in a state described by a triangular wave function ψ(x). Since the first derivative of ψ(x) is piecewise constant, and because this Hamiltonian is proportional to the second order spatial derivative, students often end up finding the expectation value to be zero—an unphysical answer. This problem provides a pedagogical application of the Dirac δ-function. By arriving at the same result via alternate pathways, this exercise reinforces students’ …

Optical Transformations In Three-Space: Simulations With A Pc, Raymond G. Wilson, Sean M. Mccreary, Jeffrey L. Thompson

Raymond Wilson