Quantization Of LC Circuit
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:Date: 1 August 2019



What is the problem ?
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Derivation
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**Step 1** Write down the Hamiltonian, and find correspondence:

.. math::
	\begin{align*}
	& H(I,Q) = {1\over 2}LI^2 + {1\over 2}{Q^2\over C}\\
	& H(p,q) = {p^2\over 2m} + {1\over 2}m\omega^2 q^2\\
	\end{align*}

.. math::
	\begin{align*}
	& L\leftrightarrow m  & C \leftrightarrow {1\over m\omega^2}\\
 	& I\leftrightarrow {p\over m}  & Q \leftrightarrow q
	\end{align*}

**Step 2** Results from Quantum-Harmonic-Oscillator then follows