Diarac notation

  • Thread starter noman3k3
  • Start date
  • #1
5
0
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:

Answers and Replies

  • #3
5
0
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
A. Neumaier
Science Advisor
Insights Author
7,568
3,418


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!!!
 
  • #5
5
0
So if states are degenerate i can have

H= [E_a 0 0 psi = [a
0 Eb 0 b
0 0 EC] c]
 
  • #6
A. Neumaier
Science Advisor
Insights Author
7,568
3,418
So if states are degenerate i can have

H= [E_a 0 0 psi = [a
0 Eb 0 b
0 0 EC] c]
Your equation looks garbled. Please use an intelligible format, to be able to answer your question.
(Probably the answer to your question is yes, but since the question isn't clear, the answer cannot be.)
 
  • #7
5
0
H= [E_a 0 0 ; 0 E_b 0; 0 0 E_c]

Psi= [a; b;c]
 
  • #8
A. Neumaier
Science Advisor
Insights Author
7,568
3,418
H= [E_a 0 0 ; 0 E_b 0; 0 0 E_c]

Psi= [a; b;c]

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.
 

Related Threads on Diarac notation

  • Last Post
5
Replies
105
Views
9K
  • Last Post
Replies
12
Views
980
  • Last Post
Replies
6
Views
783
  • Last Post
Replies
13
Views
313
  • Last Post
Replies
5
Views
820
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
612
  • Last Post
Replies
1
Views
283
Top