The wave function for a particle in a one-dimensional box is )Which statement is correct? A)This wavefunction gives the probability of finding the particle at x. B)|Ψ(x)|² gives the probability of finding the particle at x. C)|Ψ(x)|² Δx gives the probability of finding the particle between x and x + Δx. D) gives the probability of finding the particle at a particular value of x. E) gives the probability of finding the particle between x and x + Δx.

Question

Quizplus · Accepted Answer

The wave function squared, or |Ψ(x)|^2, gives the probability density of finding the particle between x and x + Δx, where Δx is an infinitesimally small interval. Therefore, |Ψ(x)| Δx gives the probability of finding the particle between x and x + Δx. Option A is incorrect because the wave function itself is not a probability, it describes the state of the particle. Option B is incorrect because it is missing the square, which is necessary to obtain the probability density. Option D is incorrect because it suggests that the wave function gives the probability at a specific point, which is not possible in quantum mechanics. Option E is incorrect because it does not include the probability density factor, |Ψ(x)|^2.

The Wave Function for a Particle in a One-Dimensional Box