Questions on Quantum Mechanics: Observables, State Functions & More

In summary, an observable in quantum mechanics is a measurable physical quantity represented by a Hermitian operator, while a state function is a mathematical function represented by a ket vector that describes the state of a quantum system. Observables are related to the uncertainty principle, which states that the more precisely we know one observable, the less precisely we can know another. Operators in quantum mechanics act on state functions and are used to represent physical observables and perform operations. The time evolution of state functions is described by the Schrödinger equation, and observables must have real eigenvalues while their eigenvectors can be complex.
  • #1
flower321
11
0
some questions...

=> How are observables related to operators in quantum mechanics?

=> what is the physical significance of state funtion in quantum mechanics?

=> why are hermition operators associated with observables in quantum mechanics?

=> what is the physical interpretation of J?
where J=L+S
=> Can we measure x ans p simultaneously with unlimited precision? give reason
 
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  • #2


flower321 said:
=> How are observables related to operators in quantum mechanics?

=> what is the physical significance of state funtion in quantum mechanics?

=> why are hermition operators associated with observables in quantum mechanics?

=> what is the physical interpretation of J?
where J=L+S
=> Can we measure x ans p simultaneously with unlimited precision? give reason

You need to show your work on these questions before we can offer any tutorial help.
 
  • #3


please reply anyone and give answer this m worry about thatttttt
 
  • #4


No.

You must show some work.
 
  • #5


which type i show work
 
  • #6


flower321 said:
which type i show work

Your response does not parse well in English.

We are asking you to show your attempts at answering your questions. You must do the work here. If you show your work, we may be able to offer hints on the parts you are having trouble with.
 

1. What is the difference between an observable and a state function in quantum mechanics?

An observable in quantum mechanics is a physical quantity that can be measured, such as position or momentum. It is represented by a Hermitian operator, which has a set of eigenvalues and corresponding eigenstates. On the other hand, a state function is a mathematical function that describes the state of a quantum system. It is represented by a ket vector in a Hilbert space and contains information about the system's physical properties.

2. How are observables related to the uncertainty principle?

The uncertainty principle states that the more precisely we know the value of one observable (such as position), the less precisely we can know the value of another observable (such as momentum). This is because the act of measuring one observable affects the state of the system, making it impossible to simultaneously know both observables with 100% certainty.

3. What is the role of operators in quantum mechanics?

Operators in quantum mechanics are mathematical objects that act on state functions and transform them into new state functions. They are used to represent physical observables and perform operations such as measurement and time evolution. Operators also play a crucial role in the mathematical formalism of quantum mechanics, allowing for the prediction of experimental outcomes.

4. How do state functions evolve over time in quantum mechanics?

In quantum mechanics, the time evolution of a state function is described by the Schrödinger equation. This equation relates the rate of change of a state function to the Hamiltonian operator, which represents the total energy of the system. Solving this equation allows us to determine the state of the system at any given time.

5. Can an observable have a complex eigenvalue?

No, an observable must have real eigenvalues. This is because the eigenvalues of an observable represent the possible outcomes of a measurement, and physical measurements can only yield real values. However, the eigenvectors (or eigenstates) of an observable can be complex.

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