Raising and Lowering Operators

  • Thread starter dFrankCalc
  • Start date
  • Tags
    Operators
In summary, The conversation is about solving a homework problem from quantum mechanics by deriving the raising and lowering operators. The process involves calculating the S+ operator based on a specific formula and using properly normalized eigenstates. However, there seems to be a discrepancy with a factor of sqrt(2) and it is suggested that this could be due to the normalization of the eigenstates.
  • #1
dFrankCalc
2
0
I am working on a homework problem from quantum mechanics. In order to solve the problem I need to derive the raising and lowering operators.

In order to to this I did the following:

S+operator = <1,i | S+operator | 1,j > where i = 1, 0, -1 with i = 1 corresponding to row one etc. I let j = 1, 0, -1 , corresponding to the columns where j = 1 is column one.

I was able to calculate every thing the same as what the book has i.e.
S+operator =hbar*sqrt(2)*[0,1,0;0,0,1; 0,0,0] except I am off by a factor of sqrt(2). Where does this factor come from?



DFrankCalc
 
Physics news on Phys.org
  • #2
Normalization probably. Are the eigenstates of your operator normalized if needed?
 
  • #3
The Sz eigen states that I used to get S+ are properly normalized.
 

FAQ: Raising and Lowering Operators

What are raising and lowering operators?

Raising and lowering operators are mathematical operators used in quantum mechanics to manipulate and transform quantum states. They are also known as ladder operators.

How are raising and lowering operators related to each other?

Raising and lowering operators are related through their commutation and anti-commutation relations. The commutator of two operators gives the result of their product minus the product of their commutators. The anti-commutator gives the result of their product plus the product of their anti-commutators.

What is the significance of raising and lowering operators in quantum mechanics?

Raising and lowering operators play a crucial role in quantum mechanics, as they allow for the creation and annihilation of particles in quantum systems. They also help in calculating the energy levels of quantum systems and in understanding the behavior of quantum systems in external fields.

How are raising and lowering operators used in solving the Schrödinger equation?

Raising and lowering operators are used in solving the Schrödinger equation by transforming the original equation into a simpler form that can be solved more easily. They also help in finding the eigenvalues and eigenfunctions of the Hamiltonian operator, which represents the total energy of a quantum system.

Can raising and lowering operators be applied to classical systems?

No, raising and lowering operators are specific to quantum mechanics and cannot be applied to classical systems. This is because classical systems do not exhibit the wave-like behavior of quantum systems, which is essential for the use of these operators.

Similar threads

I Spin operator and spin quantum number give different values, why?
Replies
12
Views
1K
I Matrix Representation of the Angular Momentum Raising Operator
Replies
7
Views
2K
I Raising and Lowering Operators
Replies
2
Views
1K
I Velocity operator, its expression and eigenvalues
Replies
27
Views
3K
I How do we know that the raising operator only raises the state by one step?
Replies
8
Views
2K
A Link between Kraus operators and PVMs
Replies
0
Views
706
A Can local conservation be verified experimentally?
Replies
12
Views
1K
QFT question about using momentum raising and lowering operators
Replies
3
Views
1K
A $S^+$ and $S^{-}$ operators formula
Replies
1
Views
783
I Displacement operation acting on individual quadrature components
Replies
3
Views
806

Hot Threads

Recent Insights

Back
Top