For example, I want to know how to quantize a free particle in the spherical coordinates. Given a classical Hamiltonian [tex]H(r, \theta, \phi, p_r, p_{\theta}, p_{\phi})[/tex], the standard procedure tells us to let [tex]r[/tex], [tex]\theta[/tex], [tex]\phi[/tex] be operators and they form a complete set. And The corresponding generalized momentums satisfy the well-known commutation relation. But starting from here, how can we obtain the specific matrix form in the coordinate representation? I looked this up in(adsbygoogle = window.adsbygoogle || []).push({}); Sakurai'smodern quantum mechanics, it seems to me that following the same reasoning there, we can get [tex]p_r=-i\hbar\frac{\partial}{\partial r}[/tex], but the expression resulting from the usual quantization procedure is [tex]p_r=-i\hbar(\frac{\partial}{\partial r}+\frac{1}{r})[/tex].

Another problem is that how to know the right form of some "combined" variables, like angular momentum, from the classical definition of those variables. The essential issue is the order of basic variables which the combined variables are made out of.

I know this is a very classical problem. But I can't find detailed presentation of the stuff. Does anyone know any textbook containing this thing? Thanks.

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# Where can I find detailed description of cononical quantization?

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