Discussion Overview
The discussion revolves around the properties of operators and eigenvalues in quantum mechanics, particularly in the context of path integrals. Participants explore the commutation relations between position and momentum operators, as well as the nature of eigenvalues derived from these operators.
Discussion Character
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant asserts that once operators act on states to produce eigenvalues, those eigenvalues commute because they are just numbers.
- Another participant challenges this view, stating that it does not make sense to multiply eigenvalues in quantum mechanics.
- Some participants note that the operators ##x## and ##p_x## do not have eigenstates in common, which complicates the discussion of their commutation.
- A later reply emphasizes that numbers and operators commute, regardless of their origin, suggesting that measured values do not affect this property.
- Participants reference a specific text, "QFT for the Gifted Amateur," to provide context for the discussion about path integrals in quantum mechanics.
Areas of Agreement / Disagreement
There is no consensus on the commutation of eigenvalues derived from operators, with some participants agreeing that eigenvalues are just numbers while others contest the validity of multiplying them in quantum mechanics.
Contextual Notes
Some participants express confusion about the relevance of the original question to path integrals, indicating a potential gap in understanding or context that remains unresolved.