Chapter 6, Problem 1Q

To determine

Whether zero probability density at certain points indicates that particle cannot move across points.

Answer to Problem 1Q

No, the zero probability density at certain point does not imply that particle cannot move across that point.

Explanation of Solution

To represent the wave function of a particle the symbol $\psi$ is used. The probability density at any given point where particle is found is represented by ${\left|\text{ψ}\right|}^2$ . The probability density is also known as the probability per unit volume.

Write the expression for probability of finding particle.

  $P_n={\left|\text{ψ}\right|}^{2}dV$

Here, $P_n$ is the probability, ${\left|\text{ψ}\right|}^2$ is the probability density and $dV$ is the volume element.

Particle inside the box means the particle is confined to one-dimensional region of space. The probability of finding the particle outside box is zero as the walls are impermeable.

Conclusion:

Thus, the zero probability density at certain point does not imply that particle cannot move across that point.