Time-independent Schrodinger equation

$H|\psi ⟩=E|\psi ⟩$, where

• $H$ is the Hamiltonian
• $E\in \mathbb{R}$ is the eigenvalue, also known as the Energy of the Eigenstate.

The time-independent Schrodinger Equation is easier to solve, and it provides the Eigenstates needed to describe the general solution.

Properties

• The energy level in a Hamiltonian is always real valued
• Eigenstates of the time independent schrodinger equation are orthogonal
• Time-independent Schrodinger equation derivation can be done via Separation of variables