Question

Can anyone help me with the derivation of the above mentioned equation please?​

Answer 1

Answer:

There is no general answer. Each equation has to be derived separately. the easiest ones are those of Euler-Lagrange type: in that case, one has simply to find a reasonable energy functional and assume that the system is trying to reach a minimum of that functional -- imposing that the functional has zero derivative will then yield an (ordinary or partial) differential equation. Many different diffusion- and wave-type equations can be obtained following this path, check e.g. the PDE book by Evans. The equations of quantum mechanics (both the Schrödinger and the Dirac ones, say) are typically NOT derived but rather axiomatically imposed