Chapter 10, Problem 10.24E

Interpretation Introduction

(a)

Interpretation:

The complex conjugate of the wave function $\Psi =4{\text{x}}^3$ is to be stated.

Concept introduction:

For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.

${\displaystyle \underset{0}{\overset{\infty }{\int }}\left(N\Psi \right)\left(N{\Psi }^{*}\right)}=1$

Where,

• $N$ is the normalization constant

• ${\Psi }^{*}$ is the conjugate of the wave function

• $\Psi$ is the wave function

Interpretation Introduction

(b)

Interpretation:

The complex conjugate of the wave function $\Psi \left(\theta \right)=e^{i\pi \theta }$ is to be stated.

Concept introduction:

For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.

${\displaystyle \underset{0}{\overset{\infty }{\int }}\left(N\Psi \right)\left(N{\Psi }^{*}\right)}=1$

Where,

• $N$ is the normalization constant

• ${\Psi }^{*}$ is the conjugate of the wave function

• $\Psi$ is the wave function

Interpretation Introduction

(c)

Interpretation:

The complex conjugate of the wave function $\Psi =4+3i$ is to be stated.

Concept introduction:

For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.

${\displaystyle \underset{0}{\overset{\infty }{\int }}\left(N\Psi \right)\left(N{\Psi }^{*}\right)}=1$

Where,

• $N$ is the normalization constant

• ${\Psi }^{*}$ is the conjugate of the wave function

• $\Psi$ is the wave function

Interpretation Introduction

(d)

Interpretation:

The complex conjugate of the wave function $\Psi =i\sin \left(3\pi \text{x}/2\right)$ is to be stated.

Concept introduction:

For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.

${\displaystyle \underset{0}{\overset{\infty }{\int }}\left(N\Psi \right)\left(N{\Psi }^{*}\right)}=1$

Where,

• $N$ is the normalization constant

• ${\Psi }^{*}$ is the conjugate of the wave function

• $\Psi$ is the wave function

Interpretation Introduction

(e)

Interpretation:

The complex conjugate of the wave function $\Psi =e^{-iEt/\hslash }$ is to be stated.

Concept introduction:

For the normalization of the wave function, the wave function is integrated as a product of its conjugate over the entire limits. It is expressed by the equation as given below.

${\displaystyle \underset{0}{\overset{\infty }{\int }}\left(N\Psi \right)\left(N{\Psi }^{*}\right)}=1$

Where,

• $N$ is the normalization constant

• ${\Psi }^{*}$ is the conjugate of the wave function

• $\Psi$ is the wave function