What is the Hamiltonian for an LC circuit?

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The Hamiltonian for an LC circuit is defined as the sum of kinetic energy (T) and potential energy (U). It is not necessary to derive the Lagrangian before calculating the Hamiltonian. The user expresses uncertainty about their solution and seeks confirmation of their approach. The discussion emphasizes the straightforward nature of deriving the Hamiltonian in this context. Understanding the relationship between energy components is crucial for accurately determining the Hamiltonian.
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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.

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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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