# Building confidence in the Dirac δ -function

@article{Gangopadhyaya2018BuildingCI,
title={Building confidence in the Dirac
$\delta$
-function},
journal={European Journal of Physics},
year={2018}
}
• Published 4 October 2018
• Physics
• European Journal of Physics
In this note we present an example from undergraduate quantum mechanics designed to highlight the versatility of the Dirac $\delta$-function. Namely, we compute the expectation value of the Hamiltonian of a free-particle in a state described by a triangular wave function $\psi(x)$. Since the first derivative of $\psi(x)$ 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…
1 Citations

## Figures from this paper

Investigation of infinitely rapidly oscillating distributions
• Mathematics
European Journal of Physics
• 2021
We rigorously investigate the rapidly oscillating contributions in the sinc-function representation of the Dirac delta function and the Fourier transform of the Coulomb potential. Beginning with a

## References

SHOWING 1-10 OF 21 REFERENCES
δ -function converging sequences
• Physics
• 2002
We discuss the usefulness and physical interpretation of a simple and general way of constructing sequences of functions that converge to the Dirac delta function. The main result, which seems to
An exact treatment of the Dirac delta function potential in the Schrödinger equation
• Physics, Mathematics
• 1975
This paper presents several cases in which the effects of the addition of a delta function potential on bound states can be computed exactly. In the case of the one dimensional Schrodinger equation,
Derivatives of the Dirac delta function by explicit construction of sequences
Explicit sequences that approach the Dirac delta function and its derivatives are often helpful in presenting generalized functions. We present a method by which a finite difference formula may be
The simplest model of the zero-curvature eigenstate
• Physics
• 2014
We consider the energy eigenvalue problem of the Dirac delta well potential, V(x) = ?V0?(x), placed between two rigid walls at x = ?a. When the strength parameter is increased, the ground state
Position-momentum uncertainty products
• Physics
• 2014
We point out two interesting features of position-momentum uncertainty product: U = ΔxΔp. We show that two special (non-differentiable) eigenstates of the Schrodinger operator with the Dirac delta
Principles of Quantum Mechanics
R. Shankar has introduced major additions and updated key presentations in this second edition of "Principles of Quantum Mechanics", including an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications.
Introduction to Quantum Mechanics (3rded.)