THE SCHRODINGER'S EQUATION

Schrödinger equation, which describes the behaviour of quantum mechanical systems. It is a partial differential equation and is widely used to calculate the behaviour of electrons in atoms, molecules, and solids.

It is written as: iℏ ∂ψ/∂t = Hψ where i is the imaginary unit, ℏ is the reduced Planck constant, ψ is the wave function of the system, t is time, and H is the Hamiltonian operator.

The wave function represents the probability distribution of a particle's position and momentum, and the Hamiltonian operator describes the total energy of the system.

In quantum mechanics, particles are described by wave functions rather than definite positions and velocities. The Schrödinger equation determines the time evolution of these wave functions and is used to calculate the probability of different states and transitions between them.

The Schrödinger equation is a cornerstone of quantum mechanics and has far-reaching implications in fields such as atomic physics, condensed matter physics, and quantum chemistry.