Final answer:
The statement is false because in quantum mechanics, eigenvalues of an operator, such as the Hamiltonian, are discrete, reflecting the quantized nature of quantum systems like the energy levels of electrons in an atom.
Step-by-step explanation:
The statement 'According to Postulate 3 of Quantum Chemistry, eigenvalues of an operator A are continuous and not discrete' is false. In quantum mechanics, the eigenvalues of a quantum operator, such as the Hamiltonian operator (which corresponds to the total energy of a system), are, in fact, discrete.
This is a reflection of the quantization inherent in quantum systems. For instance, the energy levels of an electron in an atom are quantized and correspond to discrete eigenvalues of the Hamiltonian operator. Quantum mechanics thus veers from classical mechanics where quantities can vary continuously.
In understanding the quantization of energy, it is instrumental to compare a continuous spectrum and a line spectrum. A continuous spectrum contains all wavelengths within a given range, similar to the spectrum of white light.
On the other hand, a line spectrum consists of only specific wavelengths which correspond to the energy differences between quantized energy levels of an atom. This is evident when examining emission and absorption spectra, which are known to exhibit discrete lines, each associated with transitions between energy levels unique to each element.
Therefore, the quantization of energy levels in atoms and molecules is a fundamental aspect of quantum mechanics, which contradicts the notion of continuous eigenvalues suggested by the question.