Discussion Overview
The discussion revolves around the commutation of two Hamiltonians, H and H1, for a particle in a one-dimensional box as the box length changes from "a" to "b". Participants explore the implications of this change on the eigenvectors of the Hamiltonians.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant asks whether the Hamiltonians H and H1 commute, given that they correspond to different box lengths.
- Another participant seeks clarification on the differences between H and H1.
- A participant explains that the difference lies in the boundary conditions, as the walls of the boxes are at different distances (a and b).
- There is a suggestion to write down the Hamiltonians and solve the equations to determine the relationship between them.
- A later reply indicates a misunderstanding regarding the Hamiltonians, as one participant initially believed both had the same form "p^2/2m" and therefore should have the same eigenvectors.
Areas of Agreement / Disagreement
Participants express differing views on the relationship between the Hamiltonians and their eigenvectors, indicating that the discussion remains unresolved regarding whether H and H1 have the same eigenvectors.
Contextual Notes
There are limitations in the discussion regarding the specific forms of the Hamiltonians and the boundary conditions that may affect the eigenvectors, which remain unspecified.