What is $LCAO$? Explain.

(N/A) $LCAO$ stands for Linear Combination of Atomic Orbitals.
Atomic orbitals and $\psi$: According to wave mechanics,atomic orbitals are expressed by wave functions $(\psi)$,which represent the amplitude of electron waves. These are obtained from the solution of the $Schrodinger$ wave equation.
Molecular orbitals and $LCAO$: The $Schrodinger$ wave equation cannot be solved exactly for any system containing more than one electron. Since molecular orbitals are one-electron wave functions for molecules,they are difficult to obtain directly from the $Schrodinger$ equation.
To overcome this,an approximate method known as $LCAO$ is used. It assumes that molecular orbitals can be formed by the linear combination (addition or subtraction) of atomic orbitals of the atoms involved in bonding.