Can an eigenvalue be a function?

Such an equation, where the operator, operating on a function, produces a constant times the function, is called an eigenvalue equation. The function is called an eigenfunction, and the resulting numerical value is called the eigenvalue.

Can every wave function be eigenfunction?

In this case is not an eigenfunction of the Hamiltonian. In general, the set of eigenfunctions of an operator can be used as a basis set. Any wavefunction can.

Can Wavefunctions be real?

The wavefunction is a real physical object after all, say researchers. At the heart of the weirdness for which the field of quantum mechanics is famous is the wavefunction, a powerful but mysterious entity that is used to determine the probabilities that quantum particles will have certain properties.

What is an eigenstate in quantum mechanics?

An eigenstate is a quantum state whose wave function is an eigenfunction of the linear operator that corresponds with an observable. The eigenvalue of that wave function would be the quantity you observe when you measure that observable (the eigenvalue could be a vector quantity).

What is the smallest eigenvalue in quantum mechanics?

The smallest eigenvalue is called the ground-state energy, which has a special role in many applications, including adiabatic quantum computing, where an adiabatic change of the ground state will yield the optimum of a function being studied ( Section 3.8 and Chapter 14 ). An excited state is any state with energy greater than the ground state.

What is the difference between eigenstate and superposition state?

Eigen is “one’s own” in German, so eigenstate is one’s own state, as being sane and normal and consistent over time (besides a time-dependent phase factor). On the other hand, a superposition state is a linear combination of several eigenstates, analogous to multiple personality disorder or schizophrenia in humans.

What is the eigenvalue of a linear operator?

Answer Wiki. An eigenstate is a quantum state whose wave function is an eigenfunction of the linear operator that corresponds with an observable. The eigenvalue of that wave function would be the quantity you observe when you measure that observable (the eigenvalue could be a vector quantity).