Final answer:
Quantum tunneling probability calculation for a particle encountering a potential barrier depends on several parameters and requires solving the time-independent Schrödinger equation. It is zero for E=0 eV, and for other energy values, it necessitates numerical computations.
Step-by-step explanation:
The question revolves around the concept of quantum tunneling in a quantum particle within the realm of Physics. In particular, the scenario addresses the calculation of the tunneling probability when a particle encounters a square potential barrier of a certain height and width, which is a textbook problem related to the solutions of the time-independent Schrödinger equation.
For E = 0 eV, the tunneling probability is essentially zero because the particle does not have enough energy to overcome or penetrate the potential barrier represented by V(x). To calculate the tunneling probability for E in the range of 0 – 0.5 eV, one would typically use the Schrödinger equation and find the transmission coefficient, which depends on both the height and the width of the barrier, as well as the mass and energy of the particle. Plotting this would require the use of mathematical software that applies the formulas derived from the theoretical framework of quantum mechanics.
The effective mass of GaAs and the given value for a allows us to calculate the specific conditions for the given potential barrier scenario. However, the tunneling probability can only be explicitly calculated when the energy E is specified within the range of 0 – 0.5 eV.