What is quantum mechanics? Give its primary information.

(N/A) Quantum mechanics is a theoretical framework in physics that describes the dual behavior of matter (wave-particle duality) and is based on the principles of wave motion.
It was developed independently in $1926$ by Werner Heisenberg and Erwin Schrodinger. The fundamental equation of quantum mechanics,known as the Schrodinger equation,was developed by Schrodinger,for which he was awarded the Nobel Prize in Physics in $1933$.
This equation is mathematically complex and requires advanced knowledge of calculus and differential equations to solve.
Quantum mechanics postulates that the energy of an electron in an atom is quantized. Consequently,it is impossible to determine the exact path or trajectory of an electron in an atom simultaneously with its momentum (Heisenberg's Uncertainty Principle).
For a time-independent system (such as an atom or molecule),the Schrodinger equation is expressed as:
$\hat{H}\Psi = E\Psi$
Where:
$\hat{H}$ = Hamiltonian operator (a mathematical operator representing the total energy of the system).
$E$ = Total energy of the system.
$\Psi$ = Wave function (a mathematical function that describes the quantum state of the system).
The solution of this equation provides values for $E$ and $\Psi$.
Total energy $(E)$: This accounts for the kinetic energies of all sub-atomic particles (electrons and nuclei) and the potential energy arising from the electrostatic attractions between them.
Wave function $(\Psi)$: It represents the state of the atom. While $\Psi$ itself does not have a direct physical meaning,the square of its magnitude,$|\Psi|^2$,represents the probability density of finding an electron in a specific region of space.