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In quantum mechanics at University we are learning about operators. I don't understand what you actually have to do to write an operator as a matrix...

In my notes, I'm looking at the kinetic energy operator in the Hamiltonian...

I can see for something basic - like an operator that makes things the number 3 when you have an orthonormal basis set that the matrix is simply

3 0 0

0 3 0

0 0 3

But I don't know how to adapt this to something more complex...

Thanks for your help! I hope I posted this in the right place :-s

Sam x