Eigenfunction of lti system

1. What are eigenfunctions of LTI systems?
2. What does it mean to be an eigenfunction of an operator?
3. What is an eigenfunction of a system?
4. What is an eigenfunction in quantum mechanics?

What are eigenfunctions of LTI systems?

Complex exponential signals are known as eigenfunctions of the LTI systems, as the system output to these inputs equals the input multiplied by a constant factor. Both amplitude and phase may change, but the frequency does not change.

What does it mean to be an eigenfunction of an operator?

An eigenfunction of an operator is a function such that the application of on gives. again, times a constant. (49) where k is a constant called the eigenvalue. It is easy to show that if is a linear operator with an eigenfunction , then any multiple of is also an eigenfunction of .

What is an eigenfunction of a system?

In the study of signals and systems, an eigenfunction of a system is a signal f(t) that, when input into the system, produces a response y(t) = λf(t), where λ is a complex scalar eigenvalue.

What is an eigenfunction in quantum mechanics?

In the case of Schrodinger's equation, the eigenvalues are the possible energies that the system can have if it is in a state of well-defined energy. Each eigenfunction (of the Hamiltonian) is the state of the system when its energy is equal to the associated eigenvalue.