The introduction of quantum mechanics atomic orbitals and orbital energies

4 The introduction of quantum mechanics atomic orbitals and orbital energies 

By following the rules of quantum mechanics we may convert the classical expression for the internal energy (1.6) into the Hamiltonian operator of the atom  

The Hamiltonian may be written more compactly by introducing the Laplace operator 

According to quantum mechanics, all the information that it is possible to have about the atom is contained in its wavefunction (x, y, z). If we limit ourselves to the consideration of atoms in stationary states, that is to atoms with a fixed, unchanging energy, then all possible wavefunctions are found by solving the time-independent SchrOdinger equation 

We now simplify the Hamiltonian operator, equation (1.8), by replacing pe by the real mass of the electron, me, and the Schrodinger equation becomes 

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