# Diarac notation

1. Nov 28, 2011

### noman3k3

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?

Last edited: Nov 28, 2011
2. Nov 28, 2011

### dextercioby

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

3. Nov 28, 2011

### noman3k3

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?

4. Nov 28, 2011

### A. Neumaier

Re: Hamiltonian in Dirac notation

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!!!

5. Nov 29, 2011

### noman3k3

So if states are degenerate i can have

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

6. Nov 30, 2011

### A. Neumaier

(Probably the answer to your question is yes, but since the question isn't clear, the answer cannot be.)

7. Nov 30, 2011

### noman3k3

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

Psi= [a; b;c]

8. Nov 30, 2011

### A. Neumaier

Yes, this is meaningful. The formula for H says that you represent the Hamiltonian in an eigenbasis, and the formula for psi says that the state you consider decomposes in this eigenbasis with coefficients a, b, and c.