Special conditions of a wavefunction?

[MontavonM]

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

 

[olgranpappy]

... I'm just wanting to check. Thanks in advance

no, that is not correct

 

[MontavonM]

any pointers/help you could give me?

 

[olgranpappy]

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...

 

[MontavonM]

Thank you for the help!