What is the Hamiltonian for an LC circuit?

yuvalidan
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Homework Statement


Hi i got a problem in lc circuit, I need to find the hamiltonian to this circuit , I think that I did well but I am not sure, the problem and my attempt in the following file.

Homework Equations

The Attempt at a Solution

 

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The Hamiltonian is simply
$$H=T+U$$
You don't need to find the Langrangian first.
 
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