Given an inhomogeneous ODE of the form $$a_{n}(x)y^{(n)}(x)+a_{n-1}(x)y^{(n-1)}(x)+\cdots +a_{2}(x)y''(x)+a_{1}(x)y'(x)+a_{0}(x)y(x)=f(x)$$ where ##y^{(n)}(x)\equiv \frac{d^{n}y(x)}{dx^{n}}##, why is the function ##f(x)## on the right hand side referred to as a "(adsbygoogle = window.adsbygoogle || []).push({}); source term"? In what way does itsourceleft hand side (or the function ##y(x)##)?

The reason I ask as in quantum field theory the Feynman propagator for a scalar field ##\phi (x)## can be derived by considering the Klein-Gordon equation with a so-called "source term"##J(x)##, i.e. $$\left(\Box +m^{2}\right)\phi (x)=J(x)$$ where ##\Box\equiv\eta^{\mu\nu}\frac{\partial^{2}}{\partial x^{\mu}\partial x^{\nu}}##. I'm unsure as to how this should be interpreted physically, or whether it is just a useful mathematical trick that bears no physical interpretation?! (I understand the derivation of the Feynman propagator for a scalar field from this, but I'm unsure how to motivate the introduction of the source term ##J(x)## on the right hand side of the K-G equation?!)

I originally posted this in the differential equations forum, but it was suggested that perhaps it would be more suited in this forum, given what the question is relating to.N.B.

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# What is a "source term" & what is it physically in QFT?

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