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:(adsbygoogle = window.adsbygoogle || []).push({});

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(Δt^{2}). 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Deriving the path integral

**Physics Forums | Science Articles, Homework Help, Discussion**