Discussion Overview
The discussion revolves around the application of second order time dependent perturbation theory (TDPT) to derive corrections to energy levels in quantum mechanics. Participants explore the relationship between TDPT and concepts such as the AC Stark shift, while seeking clarity on the derivation of specific equations presented in a referenced paper.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant seeks resources on deriving energy level corrections using second order TDPT, noting that traditional QM textbooks focus on population changes rather than energy level shifts.
- Another participant questions whether the situation is analogous to calculating the AC Stark shift, suggesting a potential connection.
- A participant describes their approach of calculating spin populations over time using second order TDPT and then taking the expectation value over the Hamiltonian, indicating that a direct formula may exist but would be complex and lengthy.
- Concerns are raised about the tedious nature of the calculations involved, particularly regarding the necessity of multiple integrals, which may vary in difficulty.
- There is confusion expressed about whether the state resulting from second order perturbation theory can be considered an eigenstate of the new Hamiltonian, and whether diagonalizing the time-dependent Hamiltonian is necessary for accurate energy calculations.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the existence of a direct formula for energy level corrections using second order TDPT, and there is uncertainty regarding the equivalence of different approaches to calculating energy expectations.
Contextual Notes
Participants mention the complexity of deriving formulas and the potential difficulty of integrals involved in the calculations, indicating that assumptions about the simplicity of the system may not hold in general cases.
