In quantum mechanics (QM) and quantum field theory (QFT), "quantized" and "discrete" have distinct meanings and refer to different aspects of physical quantities.
"Quantized" refers to the idea that certain physical quantities can only take on specific, discrete values rather than continuous values. This notion arises from the wave-particle duality in quantum mechanics, which states that particles and fields can exhibit both wave-like and particle-like behaviors. When a physical quantity is quantized, it means that it can only exist in discrete, quantized states or levels. These discrete values are often represented by integer multiples of a fundamental unit or quantum.
For example, in the case of energy levels in an atom, the energy of an electron orbiting the nucleus is quantized. This means that the electron can only occupy specific energy levels corresponding to certain discrete values. It cannot exist at arbitrary energy values between these levels. This behavior is captured by the concept of energy quantization in quantum mechanics.
On the other hand, "discrete" refers to something that is separate, distinct, or characterized by discontinuity. In the context of physical quantities, a discrete quantity refers to something that can only assume certain distinct values, with no intermediate values between them. These values are often separated by finite intervals or steps.
For example, in quantum field theory, the concept of particle quantization leads to the notion of discrete particle states. Each particle state is associated with specific values of the particle's properties, such as momentum and spin. These properties can only take on discrete values, and there are no intermediate values allowed.
To summarize, "quantized" refers to the discrete nature of certain physical quantities in quantum mechanics, while "discrete" describes the separation or lack of continuity between specific values of a quantity. Quantization implies discreteness, but discreteness does not necessarily imply quantization.