What Happens When the Ladder Operator Hits the Identity Operator?

In summary, the conversation discusses the meaning of the term [A,1] and its value in relation to the identity operator. The conclusion is that [A,1] equals 0 because 1 is a pure number and also represents the identity operator.
  • #1
binbagsss
1,299
11
Homework Statement
below
Relevant Equations
below
I'm just trying to follow the below
expop.png

And I understand all, I think, except what's happened to the term when A hits 1: [A,1] ?
If I'm correct basically we're just hitting on the first operator so reducing the power by one each time of the operator in the right hand bracket

thanks
 
Physics news on Phys.org
  • #2
If I understand this correctly, ##1## is the identity operator. So what would be the value of ##[A,1]##?
 
  • #3
[A,1]=0 since 1 is pure number!
 
  • #4
Abhishek11235 said:
[A,1]=0 since 1 is pure number!
omg i think i need some sleeep ! thank you haha :)
 
  • #5
binbagsss said:
omg i think i need some sleeep ! thank you haha :)
A typo! 1 here refers to identity operator as @tnich says. Anyways,final result is same
 

FAQ: What Happens When the Ladder Operator Hits the Identity Operator?

1. What is the exponential of a ladder operator?

The exponential of a ladder operator is a mathematical expression used in quantum mechanics to describe the evolution of a quantum system. It is a special type of operator that acts on a quantum state and produces a new state with a different energy.

2. How is the exponential of a ladder operator related to the energy levels of a quantum system?

The exponential of a ladder operator is closely related to the energy levels of a quantum system, as it is used to create new states with different energies by adding or subtracting a fixed amount of energy. This makes it a key tool in studying the energy spectrum of a quantum system.

3. Can the exponential of a ladder operator be used to find the probability of a quantum state?

Yes, the exponential of a ladder operator can be used to find the probability of a quantum state. This is because the squared absolute value of the exponential of a ladder operator acting on a state is equal to the probability of the state being in a particular energy level.

4. How is the exponential of a ladder operator used in quantum mechanics?

The exponential of a ladder operator is used extensively in quantum mechanics to study the behavior of quantum systems. It is used to find the energy levels of a system, calculate transition probabilities between energy levels, and describe the time evolution of a quantum state.

5. Can the exponential of a ladder operator be applied to classical systems?

No, the exponential of a ladder operator is specific to quantum mechanics and cannot be applied to classical systems. It is a mathematical tool that is used to describe the behavior of quantum systems, which have different properties and behaviors than classical systems.

Similar threads

Finding a unitary operator for quantum non-locality.
Replies
1
Views
1K
How do ladder operators generate energy values in a SHO?
Replies
2
Views
2K
A rather weird form of a coherent state
Replies
5
Views
2K
Normalization of the Angular Momentum Ladder Operator
Replies
2
Views
3K
Spherical components of a rotated operator
Replies
1
Views
1K
Ladder operators to prove eigenstates of total angular momen
Replies
2
Views
1K
Finding Eigenvalues of an Operator with Infinite Basis
Replies
1
Views
1K
Solving Ladder Operator Problem w/ 4 Terms
Replies
4
Views
3K
Is \(|p,\lambda\rangle\) an Eigenstate of the Helicity Operator?
Replies
1
Views
2K
I Displacement operation acting on individual quadrature components
Replies
3
Views
788

Hot Threads

Recent Insights

Back
Top