Time-dependent Schrödinger equation

The time-dependent Schrödinger equation is a fundamental equation in quantum mechanics that describes the dynamics of a quantum system. It provides a way to calculate the wave function of a system, which is a mathematical function that describes the probability of finding the system in a particular state.

The time-dependent Schrödinger equation is given by the following equation:

iℏ∂ψ(x,t)/∂t = Hψ(x,t)

where ψ(x,t) is the wave function of the system, ℏ is the reduced Planck constant, and H is the Hamiltonian of the system.

The time-independent Schrödinger equation is a special case of the time-dependent Schrödinger equation that applies to systems that are in a stationary state. The time-independent Schrödinger equation is given by the following equation:

Hψ(x) = Eψ(x)

where E is the energy of the system.

The time-dependent Schrödinger equation can be used to calculate the wave function of a system by solving the equation for ψ(x,t). Once the wave function is known, the probability of finding the system in a particular state can be calculated by taking the absolute square of the wave function.