Special conditions of a wavefunction?

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Discussion Overview

The discussion revolves around the conditions under which a wavefunction, dependent on multiple coordinates, can be expressed as a product of wavefunctions that depend on individual coordinates. The inquiry also touches on the implications for energy in this scenario, framed within the context of physical chemistry.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant proposes that a product wavefunction can be formed when the operators associated with the wavefunctions commute, suggesting this leads to a zero energy state.
  • Another participant challenges this assertion, indicating that it is incorrect.
  • A different participant suggests that the question likely pertains to the Hamiltonian, noting that if the Hamiltonian consists of a sum of single-particle operators, the product wavefunction can satisfy the Schrödinger equation, resulting in the total energy being the sum of individual particle energies.

Areas of Agreement / Disagreement

Participants express disagreement regarding the initial claim about the conditions for forming a product wavefunction and its implications for energy. Multiple competing views remain regarding the interpretation of the question and the role of the Hamiltonian.

MontavonM
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Under what special conditions can a wavefunction that depends on a series of coordinates be written as a product of wavefunctions that only depend on one coordinate each? What can you say about the energy in this case? (This is a study/end of the chapter question (P.Chem))... I'm thinking it's when the product wavefunction's operators commute with each other, which would make the energy zero... I'm just wanting to check. Thanks in advance
 
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MontavonM said:
... I'm just wanting to check. Thanks in advance

no, that is not correct
 
any pointers/help you could give me?
 
I think the question is worded very poorly, but probably they are looking for some statement about the Hamiltonian since they also ask about energy. For example, if the hamiltonian is the sum of single-particle operators (operators only depending on a single coordinate and momentum) then a product wavefunction can still satisfy the Schrödinger equation and the total energy is the sum of the single particle energies...
 
Thank you for the help!
 

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