Chapter 7, Problem 7D.14P

(i)

Interpretation Introduction

Interpretation:

The probability that the particle with wavefunction $\psi =N{\text{e}}^{-\kappa x}$ is inside the barrier has to be calculated.

Concept introduction:

In quantum mechanics, the wavefunction is given by $\Psi$.  The wavefunction contains all the information about the state of the system.  The wavefunction is the function of the coordinates of particles and time.  The square of the probability function, ${\left|\Psi \right|}^2$, relates to the probability density.

(ii)

Interpretation Introduction

Interpretation:

The average penetration depth of the particle with wavefunction $\psi =N{\text{e}}^{-\kappa x}$ into the barrier has to be calculated.

Concept introduction:

In quantum mechanics, the wavefunction is given by $\Psi$.  The wavefunction contains all the information about the state of the system.  The wavefunction is the function of the coordinates of particles and time.  The square of the probability function, ${\left|\Psi \right|}^2$, relates to the probability density.