Discussion Overview
The discussion revolves around the solution to the Schrödinger equation (SE) for a hypothetical atom with an extremely high atomic number (Z), specifically Z=1,000,000, and the implications of such a scenario at large quantum numbers (n) and distances from the nucleus. The focus includes theoretical considerations of electron binding energies and the stability of the nucleus.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant questions the nature of the solution to the SE for a two-body problem involving a nucleus with Z=1,000,000 and an electron at large distances.
- Another participant suggests that the basic prediction is that the nucleus would break apart quickly, and that electron binding energies would be very small.
- A clarification is made regarding the desire for a solution at high quantum numbers (n=1000 or higher) and the assumption of a stable nucleus with atomic weight 2,000,000.
- It is noted that the two-body problem can be modeled similarly to the hydrogen atom with a specific potential, but the realism of such a model is questioned.
- One participant proposes evaluating the expected momentum of the electron in the ground state to explore the feasibility of the hypothetical system.
- Another participant highlights that the concept of distance from the nucleus may be more complex than initially presented, suggesting that such exercises can reveal important nuances.
Areas of Agreement / Disagreement
Participants express differing views on the feasibility and implications of the hypothetical atom, with no consensus reached on the existence or stability of such a system.
Contextual Notes
Limitations include the complexity of finding exact solutions to the SE for multi-particle systems and the assumptions regarding the stability of the nucleus and the nature of electron binding at large distances.