In the derivation of Hamilton Jacobi Equation, it was written that with this Separation of Variable method (highlighted in red), Equation 2 can be splitted up and eventually all the variables $Q_i$ will be replaced by constants $\alpha_i$. I don't get the procedure. How does "function of $\left(q_1\right)=$ function of $\left(q_2, q_3 \ldots \ldots \ldots q_f\right)$ not involving $q_1$" come from? and should not $q_i$ instead of $Q_i$ be replaced by constants $\alpha_i$?
How Separation of Variable method eleminate all the Canonical Variables in Hamilton Jacobi Equation?
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Hi, Nomad, could you please write down in Ajax here you equation so it can be easily readable ? – EDX Jan 16 '23 at 06:04
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Hi @EDX , I have put the screenshot of the whole derivation of the equation in the my question under the link named "separation of variables". You can read it there. Thank you. – Lusypher Jan 16 '23 at 06:12