(a) Interpretation: The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated. Concept introduction: The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

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Answer 1

Question

Chapter 10, Problem 10.5E

Interpretation Introduction

(a)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(b)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(c)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

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a) The physical interpretation of the wavefunction and the fact that it is a solution of the Schroedinger equaton, which is a 2nd order differential equation, causes many restrictions on an acceptable wave function solution: (i) it must be single valued; (ii) it must be continuous; (iii) its slope must be continuous; and (iv) it must be normalizable or normalized. Sketch the following functions and check whether they can be wave function. Explain your answers. 1) 4(x) = for 0 < x <∞ 2) Y(x) = | sin(nx)|, for 0 < x< 2 3) Ҹ(x) %3D In (x), for 1 < x < 0o S0 for – 1 < x < 0 (1 for 0

2. Commuting operators. (a) Show whether the operator of the kinetic energy operator K and the momentum operator Px for a one-dimensional system commute (show every step). (b) What does the result mean (physical interpretation)?

The physical interpretation of the wavefunction and the fact that it is a solution of the Schroedinger equation, which is a 2nd order differential equation, causes many restrictions on an acceptable wave function solution: (i) it must be single-valued; (ii) it must be continuous; (iii) its slope must be continuous; and (iv) it must be normalizable or normalized. Sketch the following functions and check whether they can be wave functions. Explain your answers. (Hint, it might be useful to plot the functions).

Answer 2

Question

Chapter 10, Problem 10.5E

Interpretation Introduction

(a)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(b)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(c)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

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Answer 3

Question

Chapter 10, Problem 10.5E

Interpretation Introduction

(a)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(b)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(c)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

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Answer 4

Question

Chapter 10, Problem 10.5E

Interpretation Introduction

(a)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(b)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(c)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

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Answer 5

Chapter 10, Problem 10.5E

Interpretation Introduction

(a)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(b)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Interpretation Introduction

(c)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Answer 6

Chapter 10, Problem 10.5E

Interpretation Introduction

(a)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Answer 7

Chapter 10, Problem 10.5E

Interpretation Introduction

(a)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The examples of the functions that satisfy and do not satisfy the given requirement of acceptable wavefunctions are to be stated.

Concept introduction:

The wavefunction Ψ contains all the information about the state of the system. The wavefunction is the function of the coordinates of particles and time. The wavefunction must be single-valued, continuous, differentiable and bounded.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 10 - State the postulates of quantum mechanics...Ch. 10 - Prob. 10.2E Ch. 10 - State whether the following functions are...Ch. 10 - State whether the following functions are...Ch. 10 - Prob. 10.5E Ch. 10 - Prob. 10.6E Ch. 10 - Evaluate the operations in parts a, b, and f in...Ch. 10 - The following operators and functions are defined:...Ch. 10 - Prob. 10.9E Ch. 10 - Indicate which of these expressions yield...

Solution Summary: The author explains that the wavefunction Psi contains all the information about the state of the system.

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