How does the quantization of energy relate to quantum entanglement in a system of two particles?

Energy in quantum systems is quantized because the wavefunction must satisfy boundary conditions, giving only discrete allowed values for observables such as the Hamiltonian. When two particles share a joint wavefunction that cannot be factored into separate single‑particle states, they become entangled, meaning the state of one instantly influences the other. The discrete energy levels of each particle constrain the possible joint states, so entangled states are built from combinations of those quantized energies that satisfy the overall energy conservation. For example, two spin‑½ particles in a singlet state have each a quantized spin energy, and measuring the spin of one particle immediately fixes the spin of the other, even though their individual energies are fixed by the same quantized levels. Thus, quantization provides the discrete “building blocks” that entangled states combine, linking the two concepts.