The existence of discrete quanta, as observed in phenomena such as the quantized energy levels of atoms or the emission and absorption of photons, cannot be explained solely by the wave amplitude of a wave-like particle. The discrete nature of quanta is a fundamental aspect of quantum mechanics that goes beyond the wave-like behavior of particles.
In quantum mechanics, the energy levels of systems, such as electrons in atoms, are quantized, meaning they can only take on certain discrete values. This quantization is not solely determined by the wave amplitude of a particle but is a consequence of the underlying principles of quantum mechanics.
Quantum mechanics introduces the concept of energy quantization through the postulate that the energy of a system is quantized and can only exist in specific discrete levels. The wave function of a particle, such as an electron, describes the probabilities of different energy states and their corresponding amplitudes. However, the discrete energy levels themselves arise from the quantization of energy, which is a fundamental property of quantum systems.
In the case of photons, which are quanta of light, their energy is directly related to their frequency through Planck's constant. The energy of a photon is given by E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the photon. This relationship between energy and frequency leads to the discrete nature of the energy levels associated with photons.
Therefore, while the wave-like behavior of particles is an important aspect of quantum mechanics, the existence of discrete quanta, such as quantized energy levels, cannot be explained solely by the wave amplitude. The discrete nature of quanta arises from the fundamental principles and postulates of quantum mechanics, including energy quantization and the probabilistic nature of wave functions.