Discussion Overview
The discussion revolves around solving for new energies in a quantum system using Dirac notation, particularly after the introduction of a new potential. Participants explore methods and concepts related to the Hamiltonian and potential energy terms.
Discussion Character
- Exploratory, Technical explanation, Conceptual clarification, Homework-related
Main Points Raised
- One participant describes their problem set, indicating they have the initial energies and matrix elements but are unsure how to proceed to find the new energies after adding a new potential.
- Another participant suggests solving the equation H|psi> = E |psi> for the new Hamiltonian, which includes both the old and new potentials.
- A different participant expresses curiosity about potential tricks related to Dirac notation that might aid in the solution.
- One participant proposes that perturbation theory might be relevant if the new potential is small compared to the old potential.
- Another participant agrees with the suggestion of using perturbation theory and recommends checking Wikipedia for more information on Dirac notation.
Areas of Agreement / Disagreement
Participants express varying degrees of uncertainty about the best approach to take, with some suggesting perturbation theory while others are exploring different methods. No consensus is reached on a single method or solution.
Contextual Notes
There is an assumption regarding the size of the new potential in relation to the old potential, which may affect the applicability of perturbation theory. The discussion does not resolve whether perturbation theory is the best approach or if other methods might be more suitable.