Discussion Overview
The discussion revolves around the application of raising and lowering operators, specifically S(+) and S(-), on integer kets such as |1>, |0>, and |-1>. Participants explore the outcomes of these operations in the context of angular momentum states, particularly focusing on spin-1 and spin-1/2 systems.
Discussion Character
- Technical explanation
- Conceptual clarification
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant questions how to use the S(+) and S(-) operators on integer kets and expresses confusion about the expected outcomes.
- Another participant states that operating with S(+) on |+1> results in zero for S = 1 states and provides a link to a resource for further clarification.
- It is mentioned that for S = 1 states, a 3x3 matrix representation is appropriate.
- A participant inquires about the meaning of l in the context of spin and whether it should always be 1 for spin-1 states.
- There is a discussion about the possible values of m for spin-1/2 particles, with participants debating the correct application of the formula for angular momentum projections.
- Multiple participants express uncertainty and confusion regarding the values of m_j for different j values, leading to corrections and clarifications about the range of possible projections.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the application of the operators or the values of m_j for different spin states, with ongoing debate and corrections indicating multiple competing views.
Contextual Notes
Some participants reference specific formulas and resources, but there are unresolved questions about the definitions of l and m in the context of angular momentum, as well as the correct interpretation of the operators' effects on the kets.