Case study on the size of the particle for transmission probability to take place through the barrier

Abstract

Diffraction phenomenon occurs when the wavelength of the wave is comparable to the size of the obstacle. Tunneling through a barrier occurs when the particle size is comparable to the width of the barrier. The Transmission probability versus potential energy curve is hyperbolic in nature. This main aim of this article is to show that there is no probability of penetrating the particle through the barrier if barrier width is extremely larger and extremely smaller than the particle size. The condition for tunneling is similar to the necessary and sufficient condition for diffraction to occur. The various examples presented here shows that the penetration of the particle through the barrier is only possible when the size of the particle is comparable to the size of the barrier height. This article shows that probability occurrence, Wave-particle duality and uncertainty of a particle exists only when there is comparable size between the particle and its barrier width.