The canonical quantization procedure requires pairs of conjugate dynamical variables to be identified, which, after quantization, become operators whose commutator is $i\hbar$. How does the second quantization work? I mean just imposing a condition on the commutator leads to quantization of field, what is the underlying magic behind this prescription?
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When you have a commutator of the form, $[A,B]=i\hbar$, you can relate this to $[x,p]= [-p,x]=i\hbar$. So, as $p=\frac{\hbar}{i}\frac{\partial}{\partial x}$ you can write $B = \frac{\hbar}{i}\frac{\partial}{\partial A}$ or $-A=\frac{\hbar}{i}\frac{\partial}{\partial B}$ and proceede with the calculation of states as in ordinary quantum mechanics using your energy expression as the Hamiltonian.
Per Arve
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