Homework Help Overview
The discussion revolves around demonstrating that the inner product of two plane wave solutions, specifically ##(u_{\vec{k}},u^{*}_{\vec{k}'})##, is zero. The context involves concepts from quantum mechanics and functional analysis, particularly in relation to Hilbert spaces.
Discussion Character
- Exploratory, Assumption checking, Conceptual clarification
Approaches and Questions Raised
- Participants discuss the direct calculation of the inner product and question the formulation of the problem. There is a suggestion to clarify the Hilbert space context, whether it is ##\mathrm{L}^2(\mathbb{R}^3)## or a finite region ##D##. Additionally, there is an exploration of the integral representation of the inner product and its relation to the Dirac-delta function.
Discussion Status
The discussion is ongoing, with participants seeking clarification on the problem setup and exploring different interpretations of the inner product. Some guidance has been offered regarding the mathematical representation, but no consensus has been reached on the approach or assumptions.
Contextual Notes
There is a noted ambiguity regarding the choice of Hilbert space, which may affect the interpretation of the inner product. The original poster's question is also considered to be inadequately posed, prompting further inquiry into the specifics of the problem.