Question

Quantization is an important characteristic of systems in which a particle is bound in a small region. Why "small," and why "bound"?

Short answer

The dimensions and boundations are necessary for the particle to behave as a wave.

Step-by-step solution

Given data

Stationary state often regarded as the standing state is not just a particle that is at rest state rather, they just are the two superimposed waves having the similar frequency.

Concept of quantum mechanics

Features of quantum mechanical model:

1. The energy of an electron is quantized an electron can only have certain specific values of energy.

2. The quantized energy of an electron is the allowed solution of the Schrödinger wave equation and it is the result of wave like properties of electron.

3. As per Heisenberg's Uncertainty principle, the exact position and momentum of an electron cannot be determined.

 Step 3: Quantum mechanical model

According to the quantum mechanical model, the particle acts like a wave here. Although, they exhibit the dual nature. So, the probability density to find the particle in that particular space is fixed here the probability is stationary not the particle and it is time-independent.

Dual behavior hypothesis

Thus, using this dual-behaviour hypothesis, one can say that the particles are quantized and are represented by waves. Hence, keeping in mind the wavelength, the particles are bounded in small regions. It is important for the particle to form stationary waves in order to exhibit this wave nature.