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Given below is the wave function of a particle :

Plot of the square of psi against x: a small hump left of the origin, the tallest peak above point A, a node at point B, a small hump near C, and a thin shaded strip of width dx just left of A.

Which of the following is correct ?

  • A.The particle is more likely to be found near B
  • B.The particle is more likely to be found near A
  • C.The shaded area represents the energy of the particle when it travels through a distance dx
  • D.The shaded area represents the amplitude of the particle in an area dx

Answer: B

The particle is more likely to be found near A.

The plotted quantity is |ψ|2, the probability density. The probability of finding the particle in a small interval dx is |ψ|2dx, the shaded area. The curve has its highest value near A, so the particle is most likely to be found there.

At B the curve touches zero, a node, so the particle is least likely to be found near B. The shaded area is a probability, not an energy, and not an amplitude; the amplitude is ψ itself, whose square is plotted, and dx is a length, not an area.

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