The **Schrödinger equation** is a partial differential equation whose solution is the wave equation, which describes the probability density of a given particle over space. The general form of the Schrödinger equation is

- $ i \hbar \frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat H \Psi(\mathbf{r},t) $

where *i* is the imaginary unit, *ħ* is the reduced Planck constant, *Ψ* is the wave function, and *Ĥ* is the Hamiltonian operator (representing the total energy of the system).
In steady-state systems (where the wave equation does not depend on time, such as in an atomic or molecular orbital) this simplifies to

- $ E \Psi = \hat H \Psi $

where *E* is a constant. This is known as the time-independent Schrödinger equation.

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