The expression for the wave functions and energies as a function of quantum numbers n 1 and n 2 .

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Answer 1

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Chapter 8, Problem 4P

(a)

To determine

The expression for the wave functions and energies as a function of quantum numbers n1 and n2.

(b)

To determine

The energies of the ground state and first excited state, is either of these states degenerate.

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At time t = 0 the wave function for a particle in a box is given by the function in the provided image, where ψ1(x) and ψ1(x) are the ground-state and first-excited-state wave functions with corresponding energies E1 and E2, respectively. What is ψ(x, t)? What is the probability that a measurement of the energy yields the value E1? What is <E>?

For a particle in a 1-dimensional infinitely deep box of length L, the normalized wave function or the 1st excited state can be written as: Ψ2(x) = {1/i(2L)1/2} ( eibx -e-ibx), where b = 2π/L. Give the full expression that you need to solve to determine the probalibity of finding the particle in the 1st third of the box. Simplify as much as possible but do not solve any integrals.

The wave function for a quantum particle confined to moving in a one-dimensional box located between x = 0 and x = L is ψ(x) = A sin (nπx/L)Use the normalization condition on ψ to show that A = √2/L

Answer 2

Question

Chapter 8, Problem 4P

(a)

To determine

The expression for the wave functions and energies as a function of quantum numbers n1 and n2.

(b)

To determine

The energies of the ground state and first excited state, is either of these states degenerate.

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Answer 3

Question

Chapter 8, Problem 4P

(a)

To determine

The expression for the wave functions and energies as a function of quantum numbers n1 and n2.

(b)

To determine

The energies of the ground state and first excited state, is either of these states degenerate.

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Answer 4

Question

Chapter 8, Problem 4P

(a)

To determine

The expression for the wave functions and energies as a function of quantum numbers n1 and n2.

(b)

To determine

The energies of the ground state and first excited state, is either of these states degenerate.

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Answer 5

Chapter 8, Problem 4P

(a)

To determine

The expression for the wave functions and energies as a function of quantum numbers n1 and n2.

(b)

To determine

The energies of the ground state and first excited state, is either of these states degenerate.

Answer 6

Chapter 8, Problem 4P

(a)

To determine

The expression for the wave functions and energies as a function of quantum numbers n1 and n2.

Answer 7

Chapter 8, Problem 4P

(a)

To determine

The expression for the wave functions and energies as a function of quantum numbers n1 and n2.

Answer 8

(b)

To determine

The energies of the ground state and first excited state, is either of these states degenerate.

Answer 9

(b)

To determine

The energies of the ground state and first excited state, is either of these states degenerate.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.5 - Prob. 4E Ch. 8 - Prob. 1Q Ch. 8 - Prob. 2Q Ch. 8 - Prob. 3Q Ch. 8 - Prob. 4Q Ch. 8 - Prob. 5Q Ch. 8 - Prob. 6Q

The expression for the wave functions and energies as a function of quantum numbers n 1 and n 2 .

Solution Summary: The author describes the expression for the wave functions and energies as a function of quantum numbers n_1 and

The expression for the wave functions and energies as a function of quantum numbers n1 and n2.

The energies of the ground state and first excited state, is either of these states degenerate.

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Chapter 8 Solutions