# What are the complex conjugates of the following wavefunctions? (a) Ψ = 3 x (b) Ψ = 4 − 3 i (c) Ψ = cos 4 x (d) Ψ = − i ℏ sin 4 x (e) Ψ = e 3 ℏ ϕ (f) Ψ = e − 2 π i ϕ / ℏ

### Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437

Chapter
Section

### Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437
Chapter 10, Problem 10.25E
Textbook Problem
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## What are the complex conjugates of the following wavefunctions?(a) Ψ = 3 x (b) Ψ = 4 − 3 i (c) Ψ = cos   4 x (d) Ψ = − i ℏ   sin   4 x (e) Ψ = e 3 ℏ ϕ (f) Ψ = e − 2 π i ϕ / ℏ

Interpretation Introduction

(a)

Interpretation:

The complex conjugate of the wave function Ψ=3x 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.

0(NΨ)(NΨ*)=1

Where,

N is the normalization constant

Ψ* is the conjugate of the wave function

Ψ is the wave function

### Explanation of Solution

For the normalization of the wave function the expression is as follows.

0(NΨ)(NΨ*)=1

Where,

N

Interpretation Introduction

(b)

Interpretation:

The complex conjugate of the wave function Ψ=43i 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.

0(NΨ)(NΨ*)=1

Where,

N is the normalization constant

Ψ* is the conjugate of the wave function

Ψ is the wave function

Interpretation Introduction

(c)

Interpretation:

The complex conjugate of the wave function Ψ=cos4x 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.

0(NΨ)(NΨ*)=1

Where,

N is the normalization constant

Ψ* is the conjugate of the wave function

Ψ is the wave function

Interpretation Introduction

(d)

Interpretation:

The complex conjugate of the wave function Ψ=isin4x 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.

0(NΨ)(NΨ*)=1

Where,

N is the normalization constant

Ψ* is the conjugate of the wave function

Ψ is the wave function

Interpretation Introduction

(e)

Interpretation:

The complex conjugate of the wave function Ψ=e3ϕ 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.

0(NΨ)(NΨ*)=1

Where,

N is the normalization constant

Ψ* is the conjugate of the wave function

Ψ is the wave function

Interpretation Introduction

(f)

Interpretation:

The complex conjugate of the wave function Ψ=e2πiϕ/ 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.

0(NΨ)(NΨ*)=1

Where,

N is the normalization constant

Ψ* is the conjugate of the wave function

Ψ is the wave function

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