# Diarac notation

## Main Question or Discussion Point

I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy.

I started with Eigenvaluee problem H|Psi> = E|psi>

H = ? for state a?

SO it means that indvdually H= E (|a><a|) for state a
and for all three states i can write
H= E (|a><a|+|b><b|+|c><c|)

am i right?

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dextercioby
Homework Helper
H = E(|a><a|+...) would be a hint.

SO it means that indvdually H= E (|a><a|) for state a
and for all three states i can write
H= E (|a><a|+|b><b|+|c><c|)

am i right?

A. Neumaier
2019 Award

I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy.

I started with Eigenvaluee problem H|Psi> = E|psi>

H = ? for state a?

SO it means that indvdually H= E (|a><a|) for state a
and for all three states i can write
H= E (|a><a|+|b><b|+|c><c|)

am i right?
The H you want is most likely a 3x3 matrix. If your states a, b c are orthogonal eigenstates, the energies are the diagonal entries and the off-diagonal entries were zero. In Dirac notation, this is
H= E_a|a><a|+E_b|b><b|+E_c|c><c|

But only if the eignestates are orthogonal and eigenstates!!!

So if states are degenerate i can have

H= [E_a 0 0 psi = [a
0 Eb 0 b
0 0 EC] c]

A. Neumaier
2019 Award
So if states are degenerate i can have

H= [E_a 0 0 psi = [a
0 Eb 0 b
0 0 EC] c]
(Probably the answer to your question is yes, but since the question isn't clear, the answer cannot be.)

H= [E_a 0 0 ; 0 E_b 0; 0 0 E_c]

Psi= [a; b;c]

A. Neumaier