Schrödinger's equation

The Schrödinger equation, named after the Austrian physicist Erwin Schrödinger (1887-1961), is one of the foundations of quantum mechanics. It describes the temporal evolution of the quantum states of physical systems. This equation is deterministic, that is to say that it makes it possible to predict the state of a system at any time from its initial state.
It is written: iħ∂ψ/∂t = Hψ
where ψ is the wave function of the system, H is the Hamiltonian operator which represents the total energy of the system, ħ is the reduced Planck constant, and t is the time.
The wave function ψ is a complex mathematical function that describes the quantum state of a system. It contains all the information about the physical properties of the system, such as position, momentum, energy, spin, etc. The wave function ψ can be used to calculate the probability of finding a particle in a given region of space.
The Hamiltonian operator H represents the total energy of the system. It is defined as the sum of the kinetic and potential energies of all the particles in the system. Kinetic energy represents energy due to the motion of particles while potential energy represents energy due to interactions between particles.