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 2023-03-07 22:42:51 +0100 received badge ● Notable Question (source) 2020-12-15 07:52:54 +0100 received badge ● Popular Question (source) 2018-11-13 22:17:02 +0100 received badge ● Supporter (source) 2018-11-13 22:16:59 +0100 received badge ● Scholar (source) 2018-11-12 18:21:14 +0100 asked a question Express the derivative in the Hamiltonian operator in sage I want to compute the expectation value of the energy $\langle H \rangle$ for a quantum system with the wave function $\psi(x)$. This is done with $$\langle H \rangle = \int_{-\infty}^{\infty} \psi^* \hat{H} \psi d x$$ where $$\hat{H} = - \frac{\hbar^2}{2 m} \frac{d^2}{d x^2} + V(x)$$ is the Hamiltonian operator for some potential $V(x)$. How do I express $\frac{d}{d x}$ in sage if I don't know on which function it will be applied? I know it is possible to use psi.diff(x), but is there a way to declare the operator so that it automatically does the derivative when it is multiplied with some function? 2018-05-13 12:53:52 +0100 received badge ● Student (source) 2018-05-13 07:30:04 +0100 asked a question Define custom unit Is it possible to declare custom units that can be converted to SI base units? For example: if I want to measure time in ticks and I know that one tick is exactly one nanosecond, can I create a unit 'tick' that can later be converted to seconds? I know that a custom unit can be declared with sage: sage.symbolic.units.str_to_unit('tick') tick  I also know that predefined units can be converted, for example by sage: units.time.minute.convert(units.time.second) 60*second  However, I want to be able to declare a unit that has both its own name and that can be converted to other units. sage: tick = sage.symbolic.units.str_to_unit('tick') sage: tick tick sage: #(define relation to SI units here) sage: tick.convert(units.time.second) (ValueError: Incompatible units)  Is it possible to define a unit ‘tick’ that can be converted to seconds in this manner?