Discussion Overview
The discussion revolves around the definition and explanation of the quadrupole moment in physics, focusing on its mathematical representation and the conditions under which it is applied. Participants reference various sources, including textbooks and Wikipedia, to clarify the notation and relationships involved.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant questions whether \(\delta_{i,j}\) refers to the Kronecker delta and presents a relation for the quadrupole moment, \(Q_{i,j}=\frac{3}{2}eQ_0(x_ix_j-\frac{1}{3}\delta_{i,j})\).
- Another participant confirms that \(\delta_{i,j}\) is indeed the Kronecker delta but suggests that the initial relation is incorrect, proposing an alternative form: \(Q_{i,j}=\frac{3}{2}Q_0(\delta_{i,3}\delta_{j,3}-\frac{1}{3}\delta_{i,j})\) for a symmetric quadrupole aligned along the z-axis.
- A later reply references a formulation from Landau's "Non-relativistic Quantum Mechanics," stating \(Q_{i,j}=\frac{3}{2}Q_0(n_in_j-\frac{1}{3}\delta_{i,j})\), where \(n_i, n_j\) are components of a unit vector.
- One participant claims that their formula is a reduction of Landau's when the unit vector \(n\) is aligned in the z direction.
Areas of Agreement / Disagreement
Participants express differing views on the correct formulation of the quadrupole moment, with no consensus reached on the accuracy of the initial relation presented. Multiple competing formulations are discussed without resolution.
Contextual Notes
The discussion highlights potential limitations in the mathematical representations and assumptions regarding the alignment of the quadrupole moment, as well as the specific conditions under which these formulations apply.
