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I'm starting QFT and many books I've started to read start with the introduction of a field in a classical string model

with a Lagrange equation

[tex]L(q,\dot{q}) = \sum[\frac{m}{2}\dot{q}_{j}^{2}-\frac{k}{2}(q_{j}-q_{j+1})^{2}][/tex]

the equation of motion becomes

[tex]m \ddot{q_j}-k(q_{j+1}-2q_j + q_{j-1}) = 0[/tex]

my question is how do we get this equation of motion its a discrete derivative but I recognize this as the 3 point second derivative formula, but Lagrange formulation is only first order for the potential part

[tex]f'' = \frac{f(x+h)-2f(x)+f(x-h)}{h^2}[/tex]

any help?

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# Homework Help: QFT Classical string intro

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