The wave function ψ ∼ 12 ( x ∼ , y ∼ ) for a particle in square box should be written and should have convinced it is degenerate with ψ ∼ 21 ( x ∼ , y ∼ ) Concept introduction: The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function. The general formula of the wave function for a particle in a square box is: ψ n x n y ( x , y ) = 2 L sin ( n x π x L ) sin ( n y π y L ) Where, ψ n x n y ( x , y ) is wave function and n x , n y have values 1, 2, 3 etc. L = length of the box.

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Answer 1

Question

Chapter 4, Problem 41P

(a)

Interpretation Introduction

Interpretation:

The wave function ψ∼12(x∼,y∼) for a particle in square box should be written and should have convinced it is degenerate with ψ∼21(x∼,y∼)

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(b)

Interpretation Introduction

Interpretation:

It should be convinced that plot of ψ∼12(x∼,y∼) are same as ψ∼21(x∼,y∼) rotated by 90 degrees in the x-y plane.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(c)

Interpretation Introduction

Interpretation:

The reason should be explained physically for the relation of two sets of plots.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

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Answer 2

Question

Chapter 4, Problem 41P

(a)

Interpretation Introduction

Interpretation:

The wave function ψ∼12(x∼,y∼) for a particle in square box should be written and should have convinced it is degenerate with ψ∼21(x∼,y∼)

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(b)

Interpretation Introduction

Interpretation:

It should be convinced that plot of ψ∼12(x∼,y∼) are same as ψ∼21(x∼,y∼) rotated by 90 degrees in the x-y plane.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(c)

Interpretation Introduction

Interpretation:

The reason should be explained physically for the relation of two sets of plots.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

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Answer 3

Question

Chapter 4, Problem 41P

(a)

Interpretation Introduction

Interpretation:

The wave function ψ∼12(x∼,y∼) for a particle in square box should be written and should have convinced it is degenerate with ψ∼21(x∼,y∼)

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(b)

Interpretation Introduction

Interpretation:

It should be convinced that plot of ψ∼12(x∼,y∼) are same as ψ∼21(x∼,y∼) rotated by 90 degrees in the x-y plane.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(c)

Interpretation Introduction

Interpretation:

The reason should be explained physically for the relation of two sets of plots.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

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Answer 4

Question

Chapter 4, Problem 41P

(a)

Interpretation Introduction

Interpretation:

The wave function ψ∼12(x∼,y∼) for a particle in square box should be written and should have convinced it is degenerate with ψ∼21(x∼,y∼)

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(b)

Interpretation Introduction

Interpretation:

It should be convinced that plot of ψ∼12(x∼,y∼) are same as ψ∼21(x∼,y∼) rotated by 90 degrees in the x-y plane.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(c)

Interpretation Introduction

Interpretation:

The reason should be explained physically for the relation of two sets of plots.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 4, Problem 41P

(a)

Interpretation Introduction

Interpretation:

The wave function ψ∼12(x∼,y∼) for a particle in square box should be written and should have convinced it is degenerate with ψ∼21(x∼,y∼)

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(b)

Interpretation Introduction

Interpretation:

It should be convinced that plot of ψ∼12(x∼,y∼) are same as ψ∼21(x∼,y∼) rotated by 90 degrees in the x-y plane.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

(c)

Interpretation Introduction

Interpretation:

The reason should be explained physically for the relation of two sets of plots.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

Answer 6

Chapter 4, Problem 41P

(a)

Interpretation Introduction

Interpretation:

The wave function ψ∼12(x∼,y∼) for a particle in square box should be written and should have convinced it is degenerate with ψ∼21(x∼,y∼)

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

Answer 7

Chapter 4, Problem 41P

(a)

Interpretation Introduction

Interpretation:

The wave function ψ∼12(x∼,y∼) for a particle in square box should be written and should have convinced it is degenerate with ψ∼21(x∼,y∼)

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

Answer 8

(b)

Interpretation Introduction

Interpretation:

It should be convinced that plot of ψ∼12(x∼,y∼) are same as ψ∼21(x∼,y∼) rotated by 90 degrees in the x-y plane.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

Answer 9

(b)

Interpretation Introduction

Interpretation:

It should be convinced that plot of ψ∼12(x∼,y∼) are same as ψ∼21(x∼,y∼) rotated by 90 degrees in the x-y plane.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

Answer 10

(c)

Interpretation Introduction

Interpretation:

The reason should be explained physically for the relation of two sets of plots.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

Answer 11

(c)

Interpretation Introduction

Interpretation:

The reason should be explained physically for the relation of two sets of plots.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

Answer 12

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Answer 13

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Answer 14

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Answer 15

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