Discussion Overview
The discussion revolves around the application of the Schrödinger equation to understand the probability distribution of electrons as they transition between atoms, particularly in the context of electrical conduction in materials like wires.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
Main Points Raised
- One participant questions whether the Schrödinger equation can show the probability distribution of an electron jumping between atoms, particularly in a circuit.
- Another participant suggests that while the answer is "in principle yes," practical applications may require a deeper understanding of solid-state physics, including concepts like valence and conduction bands.
- A participant expresses curiosity about the movement of electrons within a wire and proposes that simulations could illustrate how the probability distribution changes along a grid of atoms, given the influence of surrounding particles.
- One participant mentions that the analysis could be performed using a tight binding model, noting that the Hamiltonian used may differ from the conventional position space Hamiltonian.
Areas of Agreement / Disagreement
Participants do not reach a consensus; multiple competing views remain regarding the applicability of the Schrödinger equation and the models that may be used to analyze electron behavior in materials.
Contextual Notes
There are limitations related to the definitions of the Schrödinger equation and the assumptions underlying different models, such as the tight binding model versus traditional Hamiltonians.