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On the attached picture I have started trying to derive the path integral but I don't know how I get further. Can anyone help me? Also I have used that:
exp(-iHΔt/ħ) = exp(-i(T+V)Δt/ħ) = exp(-iTΔt/ħ)exp(-iVΔt/ħ)
But my book says that this identity is only correct to first order, i.e. there is an O(Δt2). What is the general identity for factoring the exponential of a sum of operators?
But please help me to make progress in my derivation of the path integral, since I would like to understand how it comes about.
exp(-iHΔt/ħ) = exp(-i(T+V)Δt/ħ) = exp(-iTΔt/ħ)exp(-iVΔt/ħ)
But my book says that this identity is only correct to first order, i.e. there is an O(Δt2). What is the general identity for factoring the exponential of a sum of operators?
But please help me to make progress in my derivation of the path integral, since I would like to understand how it comes about.
