Question

How does decreasing the height of the walls of a box influence the probability distribution of a quantum mechanical particle-in-a-box? [walls, potential energy, infinite, finite, tunneling, probability, wavelength, energy...]

Answer 1

Suppose Potential walls are infinity, the particle is simply bounded inside the region (box) which implies that the probability of finding the particle inside the box is literally 1.

when the Potential is decreased to finite non-zero values, the particle's wavefunction exponentially decays outside the walls implying the particle has a finite non-zero probability of existing outside the box. This probability is related to the difference in Energy of the particle and Potential barrier.

As the potential gets smaller, it becomes close to the energy of the particle which thus increases the extent till where the wavefunction of the particle will penetrate outside the potential walls thereby implying that the probability of the particle existing outside has increased.