What is Schrodinger equation?

Suppose a particle of mass m, constrained to move along the x-direction in the region of the potential V. Then Schrodinger equation for this particle is,

$$ i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \psi}{\partial x^2} + V\psi$$

\(i\) is the square root of -1 and \(\hbar = \frac{h}{2\pi}\).
\(\psi\) is the wave function of the particle.
V is the specified potential.