Not sure where this final Hamiltonian came from

[SamRoss]

Homework Statement

In PDF

Relevant Equations

In PDF

Here's the problem and the solution provided online by the author (the problem numbers are different but it's the same question). I think I'm okay up until the last step where he declares the Hamiltonian is (1 1 1 -1). Where did he get those components?

 

[PeroK]

Isn't that implicit in the original statement about $H$?

 

[TSny]

Where did he get those components?

The matrix element $H_{12}$, for example, equals $\langle 1|\hat H | 2 \rangle$. See what you get when you evaluate $\langle 1|\hat H | 2 \rangle$ using the given expression for $\hat H$.

 

[SamRoss]

The matrix element $H_{12}$, for example, equals $\langle 1|\hat H | 2 \rangle$. See what you get when you evaluate $\langle 1|\hat H | 2 \rangle$ using the given expression for $\hat H$.

Oh okay, it wasn't that bad after all.

Isn't that implicit in the original statement about $H$?

I suppose it was. Finding the eigenvectors was apparently unnecessary for finding H.

Thanks everyone!