Chapter 10, Problem 10.69E

Interpretation Introduction

Interpretation:

The value of $\langle E\rangle$ for ${\Psi }_1$ of a particle-in-a-box is to be evaluated. Whether the corresponding value is exactly the same as the eigenvalue for energy obtained using the Schrödinger equation is to be shown. The corresponding conclusion is to be justified.

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.