Schrodinger Equation

$i\hslash \dot{\psi }=H\psi$ defines the time evolution of a Quantum state $\psi$

Different systems make use of the above equation by specifying different Hamiltonians. As an example, the Schrodinger equation for a single non-relativistic Particle under a time dependent Potential $V(x,t)$ is given by: $ih\frac{\partial }{\partial t}\Psi (x,t)=\left[-\frac{h}{2m}\frac{{\partial }^2}{\partial x^2}+V(x,t)\right]\Psi (x,t)$where:

• $H$ is the Hamiltonian
• $\hslash$ is Planck’s reduced constant
• $V$ is the Potential energy