A quantum well is a potential well that confines particles, such as electrons, to a very small region of space — typically in semiconductor structures. Why Energy Levels are Quantized:
In classical mechanics, particles can have any energy, but in quantum mechanics, when a particle is confined to a small region (like a well), only specific energy states are allowed.
This is because the electron’s wavefunction must satisfy boundary conditions — it must fit “neatly” within the well, leading to discrete (quantized) energy levels.
The smaller (narrower) the well, the greater the energy spacing between allowed levels.
These quantized levels are highly dependent on the well's width and depth.
Why the Other Options Are Incorrect:
(A) Continuous: Applies to free particles, not confined systems like a quantum well.
(C) Defined by the Fermi level: The Fermi level defines the highest filled state at 0 K but does not determine the actual energy levels in the well.
(D) Independent of the well's dimensions: In reality, the dimensions strongly affect the quantized energy values — narrower wells yield higher energy spacing.
Thus, electrons in a quantum well can only occupy quantized energy levels due to confinement.
