Operators and eigenstates

In summary, operators in quantum mechanics are mathematical symbols or functions that represent physical observables or properties of a system. They are used to describe the behavior of quantum systems and calculate the probability of observing a certain value. Eigenstates are quantum states associated with a definite value of a physical observable and are acted upon by operators to reveal the value of the observable. An operator can have multiple eigenstates with different eigenvalues.
  • #1
Slepton
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I am confused about operators and eigenstates. What does "an operator has two normalized eigenstates" mean ? Is there a way I can make a physical interpretation ? How are measurements made with these ?
 
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  • #2
Keep reading and learning: these question are answered.
 
  • #3
Slepton said:
What does "an operator has two normalized eigenstates" mean ? Is there a way I can make a physical interpretation ?
It means that when you make the measurement corresponding to the operator you will measure one of two values.
 

1. What is an operator in quantum mechanics?

An operator in quantum mechanics is a mathematical symbol or function that represents a physical observable or property of a system. It acts on a quantum state to produce another quantum state or a numerical value.

2. How are operators used in quantum mechanics?

Operators are used to describe the behavior of quantum systems, including the movement and interactions of particles. They are also used to calculate the probability of observing a particular value for a physical quantity.

3. What is an eigenstate in quantum mechanics?

An eigenstate is a quantum state that is associated with a definite value of a physical observable, such as position or momentum. It is a solution to the Schrödinger equation and represents the most probable state of a system.

4. How are eigenstates related to operators?

Eigenstates are the states that are acted upon by operators to produce definite values of physical observables. The operator "measures" the eigenstate, revealing the value of the observable that the state represents.

5. Can an operator have multiple eigenstates?

Yes, an operator can have multiple eigenstates associated with it. These eigenstates may have different eigenvalues, which represent the different possible values of the physical observable that the operator represents.

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