Not sure where this final Hamiltonian came from

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SamRoss
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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?
 

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  • #2
PeroK
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Isn't that implicit in the original statement about ##H##?
 
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TSny
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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##.
 
  • #4
SamRoss
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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!
 

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