- #1
terp.asessed
- 127
- 3
Could someone please explain Hψ = Eψ? I understand that H = Hamiltonian operator and ψ is a wavefunction, but how is H different from E? I am confused. I am trying to understand "Hψ = Eψ" approach
catsarebad said:Hψ = Eψ
is an eigenvalue problem
you can read about it here
http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors
so,
H is the eigenvector and E is it's corresponding eigenvalue. eigenvalues are constants. for each eigenvalue you can find a corresponding eigenvector.
again, think of it like a eigenvalue problem and that should be clear.
terp.asessed said:Wait, E is a constant?
An eigenfunction of Hamiltonian is a mathematical function that represents a stationary state of a quantum mechanical system. It is a solution to the Schrödinger equation, which describes the time evolution of a quantum system.
Eigenfunctions of Hamiltonian are associated with specific energy values, known as eigenvalues. The eigenvalue for an eigenfunction is the energy of the system in that particular state.
Yes, an eigenfunction of Hamiltonian can be represented as a linear combination of multiple states. This superposition of states allows for a more accurate description of the system's behavior.
Yes, eigenfunctions of Hamiltonian are unique for a given system. This means that no two eigenfunctions will have the same energy value and they are orthogonal to each other.
Eigenfunctions of Hamiltonian are a fundamental concept in quantum mechanics and are used to describe the energy states of a system. They are also used to calculate the probability of a system being in a particular state and to predict the behavior of the system over time.