{wiki}

One dimension in <position representation>:
$$
\hat{p} = - i \hbar \pdv{}{x}
$$

In three dimensions In position representation, we define it by using the <gradient>, and so we see that 
$$
\hat{p} = - i \hbar \pdv{}{x}
$$

\Video[https://www.youtube.com/watch?v=Egu4i8umpoM]
{title=Position and Momentum from Wavefunctions by <Faculty of Khan> (2018)}
{description=Proves in detail why the <momentum operator> is $\pdv{}{x}$. The starting point is determining the time <derivative> of the <expectation value> of the <position operator>.}


Momentum operator

TODO what it means to solve an Ising model in general?

https://stanford.edu/~jeffjar/statmech/lec4.html gives some good notions:
* $<\sigma_i>$ is the <expectation value> of the value. It is therefore a number between -1.0 an and 1.0, -1.0 means everything is always down, 0.0 means half up half down, and 1.0 means all up
* $<\sigma_i \sigma_j>$: correlation between neighboring states. TODO.


Ciro Santilli @cirosantilli 37

 Incoming links: Expectation value