European Journal of Physics
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’ confidence in the Dirac δ-function and highlights its efficiency and elegance.
Gangopadhyaya, Asim and Rasinariu, Constantin, "Building Confidence in the Dirac δ-function" (2018). Physics: Faculty Publications and Other Works. 50.
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© European Physical Society 2018
Author Posting. © European Physical Society 2018. This article is posted here by permission of the European Physical Society for personal use, not for redistribution. The article was published in the European Journal of Physics, 2018, https://doi.org/10.1088/1361-6404/aaddcd