Discussion Overview
The discussion revolves around an integral from Quantum Mechanics, specifically the integral \(\int_{-\infty}^{\infty} A e^{-(x-a)^2} dx\). Participants explore the availability of online integral tables and methods for solving the integral, including substitutions and transformations.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- Jeremy inquires about accessible online integral tables for a specific integral from Quantum Mechanics.
- Some participants question whether \(A\) is a constant or a matrix, with Daniel suggesting it should be clarified if \(A\) is dependent on \(x\).
- Jeremy clarifies that \(A\) is indeed a constant, which leads to further discussion on the integral's solvability.
- Daniel proposes that the integral can be reduced to a Poisson integral using a substitution and applying the theorem of Fubini and polar coordinates.
- Another participant suggests squaring the integral and transforming to polar coordinates, indicating that no antiderivative exists in terms of familiar functions.
- A specific case is mentioned where if \(a = 0\) and \(A = 1\), the result is \(\sqrt{\pi}\).
Areas of Agreement / Disagreement
Participants generally agree on the nature of \(A\) as a constant and discuss methods for solving the integral, but there is no consensus on the existence of an antiderivative or the best approach to take.
Contextual Notes
The discussion includes assumptions about the nature of \(A\) and the conditions under which the integral can be simplified, but these aspects remain unresolved in terms of broader applicability.