Quantum mechanics is based on fundamental equation which is called:

Hint:Quantum mechanics is a fundamental physics theory that describes the physical properties of nature on atomic and subatomic scales. All quantum physics, including quantum chemistry, quantum field theory, quantum technology, and quantum information science, is built on this basis.

Complete answer:
Quantum mechanics is a branch of physics that studies the behaviour of matter and light on an atomic and subatomic level. It tries to explain and classify the properties of molecules and atoms as well as their constituents, which include electrons, protons, neutrons, and other more esoteric particles including quarks and gluons. These properties include the interactions of the particles with one another and with electromagnetic radiation (i.e., light, X-rays, and gamma rays).

Quantum mechanics is based on the Schrodinger equation, which is a fundamental equation.
In classical mechanics, the Schrodinger equation plays the function of Newton's laws and energy conservation, predicting the potential behaviour of a complex system. It is a wave equation in terms of the wavefunction that predicts the likelihood of events or outcomes analytically and precisely. The precise outcome is not predetermined, but the Schrodinger equation can predict the distribution of outcomes provided a large number of events.
Kinetic energy + Potential energy = E

The kinetic and potential energies are combined into the Hamiltonian, which acts on the wavefunction to cause it to evolve in time and space. The Schrodinger equation gives the system's quantized energies as well as the wavefunction's structure, which can be used to calculate other properties. It is written as –
$H\psi = E\psi $
Where $H = $Hamiltonian Operator, $\psi = $ Wave function and $E = $ Energy.

Note:In terms of concept, the Schrödinger equation is the quantum equivalent of Newton's second law of classical mechanics. Newton's second law predicts the direction a given physical structure will follow over time based on a set of known initial conditions.