The wave function ψ ( x ) for a quantum particle in state n = 4 in a finite potential well.

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Answer 1

Question

Chapter 41, Problem 29P

(a)

To determine

The wave function ψ(x) for a quantum particle in state n=4 in a finite potential well.

(b)

To determine

The probability density function |ψ(x)|2 for a quantum particle in state n=4 in a finite potential well.

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An electron is confined to move in the xy plane in a rectangle whose dimensions are Lx and Ly. That is, the electron is trapped in a two dimensional potential well having lengths of Lx and Ly. In this situation, the allowed energies of the electron depend on two quantum numbers nx and ny and are given by E = h2/8me (nx2/Lx2 + ny2/Ly2)Using this information, we wish to find the wavelength of a photon needed to excite the electron from the ground state to the second excited state, assuming Lx = Ly = L. (a) Using the assumption on the lengths, write an expression for the allowed energies of the electron in terms of the quantumnumbers nx and ny. (b) What values of nx and ny correspond to the ground state? (c) Find the energy of the ground state. (d) What are the possible values of nx and ny for the first excited state, that is, the next-highest state in terms of energy? (e) What are the possible values of nx and ny for thesecond excited state?…

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Answer 2

Question

Chapter 41, Problem 29P

(a)

To determine

The wave function ψ(x) for a quantum particle in state n=4 in a finite potential well.

(b)

To determine

The probability density function |ψ(x)|2 for a quantum particle in state n=4 in a finite potential well.

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Answer 3

Question

Chapter 41, Problem 29P

(a)

To determine

The wave function ψ(x) for a quantum particle in state n=4 in a finite potential well.

(b)

To determine

The probability density function |ψ(x)|2 for a quantum particle in state n=4 in a finite potential well.

Expert Solution & Answer

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Answer 4

Question

Chapter 41, Problem 29P

(a)

To determine

The wave function ψ(x) for a quantum particle in state n=4 in a finite potential well.

(b)

To determine

The probability density function |ψ(x)|2 for a quantum particle in state n=4 in a finite potential well.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 41, Problem 29P

(a)

To determine

The wave function ψ(x) for a quantum particle in state n=4 in a finite potential well.

(b)

To determine

The probability density function |ψ(x)|2 for a quantum particle in state n=4 in a finite potential well.

Answer 6

Chapter 41, Problem 29P

(a)

To determine

The wave function ψ(x) for a quantum particle in state n=4 in a finite potential well.

Answer 7

Chapter 41, Problem 29P

(a)

To determine

The wave function ψ(x) for a quantum particle in state n=4 in a finite potential well.

Answer 8

(b)

To determine

The probability density function |ψ(x)|2 for a quantum particle in state n=4 in a finite potential well.

Answer 9

(b)

To determine

The probability density function |ψ(x)|2 for a quantum particle in state n=4 in a finite potential well.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 41.1 - Prob. 41.1QQ Ch. 41.2 - Prob. 41.2QQ Ch. 41.2 - Prob. 41.3QQ Ch. 41.5 - Prob. 41.4QQ Ch. 41 - Prob. 1OQ Ch. 41 - Prob. 2OQ Ch. 41 - Prob. 3OQ Ch. 41 - Prob. 4OQ Ch. 41 - Prob. 5OQ Ch. 41 - Prob. 6OQ

The wave function ψ ( x ) for a quantum particle in state n = 4 in a finite potential well.

Solution Summary: The author illustrates the wave function for a quantum particle in state n=4, and the probability density function.

The wave function ψ(x) for a quantum particle in state n=4 in a finite potential well.

The probability density function |ψ(x)|2 for a quantum particle in state n=4 in a finite potential well.

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Chapter 41 Solutions