- #1

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H = -ħ

^{2}/2m * (∂

^{2}/∂x

_{1}

^{2}+ ∂

^{2}/∂x

_{2}

^{2})

Hψ=Eψ

∂

^{2}ψ/∂x

_{1}

^{2}+ ∂

^{2}ψ/∂x

_{2}

^{2}= kψ, where k=-2mE/ħ

^{2}

I got up to here, where I need to write down a form for ψ to take. Both textbooks I referred to (Griffiths and Shankar) use the example of a wavefunction for 2 distinguishable particles before discussing the 2-term form for a wavefunction of 2 indistinguishable particles. Apparently for 2 distinguishable particles, ψ(x

_{1},x

_{2})=ψ

_{a}(x

_{1})ψ

_{b}(x

_{2}), but I don't understand the reasoning behind writing it as a product of the individual wavefunctions. Griffiths discusses it a little bit in footnote 2, but I don't follow it. I do understand the later part about writing ψ for indistinguishable particles as a sum of the two products, but I don't understand why each term is written as a product in the first place.