GroundState

In quantum mechanics, the energy of a state is the eigenvalue associated with its eigenfunction. The Hamiltonian operator, $H$, describes the system's total energy. Eigenfunctions of $H$, solutions to the Schrödinger equation, correspond to the system's states, and their eigenvalues are the energies of these states.

• The ground state is the eigenfunction of $H$ with the lowest eigenvalue, known as the zero-point energy.
• Excited states have higher eigenvalues than the ground state.

Each eigenfunction $\psi$ of $H$ has a corresponding eigenvalue $E$, where:

$$ H\psi = E\psi $$

$E$ is the energy of the state described by $\psi$.