>>
>> IIUC, this is the "dequantised" version of X P, which is a perfectly
>> well-defined quantum operator. "Obviously", (x * d_dx)(f) should
>> return x * f'(x), but I see no way to make it work in your design.
>
> I noticed this too. It wouldn't really be possible to make an
> "operator of operators", like a differential equation, because
> something like (Derivative + f)(f)(x) would return Derivative(f(x), x)
> + f(f(x)).  I don't really see how one could do this with Lambdas
> either, btw.
>

The comparison with quantum mechanics is very flawed: X and P are both
hermitian operators (the same mathematical object). However I was
hasty in my first answer:

x is a scalar field
d_dx is a vector field
x * d_dx should be a vector field

This is related to the example that Aaron gave. I have a solution that
works great if one assumes that the user will not do stupid things and
that fails completely without this assumption. Please comment on this:

https://krastanov.wordpress.com/2012/05/27/scalar-and-vector-fields-in-sympy-first-steps/

The part where I explain the construction of scalar and vector fields.
I would like to know whether you are against this design.

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