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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Students have asked these similar questions

Imagine a particle free to move in the x direction. Which of the following wavefunctions would be acceptable for such a particle? In eachcase, give your reasons for accepting or rejecting each function. (i) Ψ(x)=x2; (ii) Ψ(x)=1/x; (iii) Ψ(x)=e-x^2.

A normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2 sin(πx/L). Suppose that L = 10.0 nm. Calculate the probability that the particle is (a) between x = 4.95 nm and 5.05 nm, (b) between x = 1.95 nm and 2.05 nm, (c) between x = 9.90 nm and 10.00 nm, (d) between x = 5.00 nm and 10.00 nm.

The ground-state wavefunction for a particle confined to a one dimensional box of length L is Ψ =(2/L)½ sin (πx/L) Suppose the box 10.0 nm long. Calculate the probability that the particle is: (a) between x = 4.95 nm and 5.05 nm (b) between 1.95 nm and 2.05 nm, (c) between x = 9.90 and 10.00 nm, (d) in the right half of the box and (e) in the central third of the box.

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.

Expert Solution & Answer

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Check out a sample textbook solution

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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.

Expert Solution & Answer

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Check out a sample textbook solution

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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

See solution

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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