Discussion Overview
The discussion revolves around the analogy between non-linear least squares curve fitting and Matrix Mechanics in quantum physics. Participants explore how matrix mechanics might relate to observed results and the role of wave functions, eigenstates, and the Schrödinger Equation in this context.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant describes their experience with non-linear least squares curve fitting and questions whether Matrix Mechanics operates similarly by fitting observed results to a model matrix.
- Another participant argues that the analogy of "fitting" is not appropriate for understanding Heisenberg's reasoning and provides a mathematical framework for expressing quantum states using a discrete basis set.
- Questions arise regarding whether eigenstates of the Hamiltonian are known before conducting an experiment or if they are determined by the results of the experiment.
- Some participants clarify that eigenstates are determined by the Hamiltonian and the characteristics of the physical system, and that the state can be known or unknown depending on preparation.
- There is a discussion about the purpose of the Schrödinger Equation, with some stating it allows for the prediction of future states of a system and helps identify wave functions corresponding to measured energies.
- One participant expresses a realization about the eigenfunction nature of quantum systems, suggesting it simplifies analysis by restricting states to predefined eigenstates or their linear combinations.
Areas of Agreement / Disagreement
Participants express differing views on the appropriateness of the fitting analogy and the role of eigenstates in quantum mechanics. The discussion remains unresolved regarding the relationship between Matrix Mechanics and curve fitting, as well as the implications of the Schrödinger Equation.
Contextual Notes
Participants highlight the dependence of eigenstates on the Hamiltonian and the physical system, but the discussion does not resolve how these concepts interrelate with the analogy proposed by the initial poster.