CALCULATION AND VISUALIZATION OF QUANTUM-MECHANICAL TUNNEL EFFECT
Ключевые слова:
wave packet, reflected wave, transmitted wave, potential barrier, barrier width, probability.Аннотация
The article presents calculations and visualization of wave packet tunneling through the potential
barrier of various widths done by using the MATLAB software. The graph of distribution of the probability density
along barrier width is obtained in two and three dimensions. The article contains materials about quantummechanical tunnel effect such as the reflection of the part of the wave packet from the potential barrier and passing
through the barrier of the other part. Calculations and visualization of the tunneling process are performed for
various widths of the barrier. Figures given in the article show the probability of finding the particle at a certain time,
i.e. the square of the absolute value of the state vector 2
. The part of the total number of particles tunnels through
barrier, the other part reflects from it. The probability of tunneling increases with decrease of the barrier width. The
detailed analysis of the graphs reveals that the wave function exponentially decreases inside the potential barrier
therefore the observation of this effect requires a rather small width of the barrier. Students are offered to develop
programs for various widths of the potential barrier. Results of experiments are used during the study of the quantum
mechanics.
