Chapter 11, Problem 11.55E

Interpretation Introduction

(a)

Interpretation:

The energy of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The energy for the 3-D rotational motion is given by,

$E=\frac{l\left(l+1\right){\hslash }^2}{2I}$

The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

Interpretation Introduction

(b)

Interpretation:

Total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The total angular momentum for the 3-Dimensional system is given by,

$L=\sqrt{l\left(l+1\right)}\hslash$

The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.

Interpretation Introduction

(c)

Interpretation:

The z-component of the total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,

${\widehat{L}}_z=m_l\hslash$