Answer:
The mathematical expression for the quantization of energy in a system described by the Schrödinger equation is given by the eigenvalue equation:
HΨ = EΨ
Where H is the Hamiltonian operator, Ψ is the wave function, and E is the eigenvalue that represents the quantized energy of the system.
The concept of quantized energy levels in an atom is related to the quantization of energy in the Schrödinger equation. In quantum mechanics, atoms can only exist in certain energy levels or states, which are determined by the solutions to the Schrödinger equation. These energy levels are quantized, meaning that the energy can only take on specific values, and not any value in between. This results in the characteristic spectra of atomic systems, where the electrons in an atom can only transition from one energy level to another by absorbing or emitting a photon with an energy that corresponds to the difference in energy between the two levels.
In summary, the quantization of energy in a system described by the Schrödinger equation is the foundation for the concept of quantized energy levels in atoms, which has important implications for our understanding of the behavior of atoms and the properties of materials.