Particle in a box: A particle trapped in a one-dimensional finite potential well with U₀= 0 in the region 0

Question

Particle in a box: A particle trapped in a one-dimensional finite potential well with U₀= 0 in the region 0 < x < L, and finite U₀ everywhere else, has a ground state wavenumber, k. The ground state wavenumber for the same particle in an infinite one-dimensional potential well of width L, would be A) less than k. B) greater than k. C) equal to k. D) There is not enough information to determine.

Quizplus · Accepted Answer

The ground state energy of a particle in a finite potential well is always greater than the ground state energy of a particle in an infinite potential well of the same width. This means that the wavenumber, which is related to the energy by E = (h^2/8m)L^2(k^2), is greater in the infinite potential well than in the finite well. Therefore, the answer is B, greater than k.

Particle in a Box: a Particle Trapped in a One-Dimensional