a) The radial probability density P ( r ) for ψ 210 . b) The radial probability density P ( r ) for ψ 21 + 1 and ψ 21 - 1 . c) To show that each P ( r ) is consistent with the corresponding dot plot. d) To show that the sum of the radial probability densities is spherically symmetric.

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Answer 1

Question

Chapter 39, Problem 45P

To determine

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.

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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 the quant numbers Nx and Ny, the allowed energies are given by E = H^2/8Me ( Nx^2/ Lx^2 + Ny^2/Ly^2) i) assuming Lx and Ly =L. Find the energies of the lowest for all energy levels of the electron ii) construct an energy level diagram for the electron and determine the energy difference between the second exited state and the ground state?

a) Determine the quantum mechanical operators for the following: Lx=yPz - ZPy That is, find Îx = ŷêz - 2py where x = x êx = ћд і дх Ly = Zpx - xPz Îy = 2px - xôz ŷ = y Py = b) Determine the commutator i.e. [Î¸‚Î‚] - - = x 'y ħ a і ду 2 = z Lz = xpy - ypx Û₂ = âÔy – ŷÂx êz = (Î‚Î‚¸ – Î¸Îx)ƒ(xx.2) = ? L y ħ ə і дz

I need to determine if the given state is entangled or not. |ϕ1⟩ = (1 / √3) |00⟩ − (i / √3) |01⟩ + (1+ i / √6) |11⟩

Answer 2

Question

Chapter 39, Problem 45P

To determine

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.

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Answer 3

Question

Chapter 39, Problem 45P

To determine

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 39, Problem 45P

To determine

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.

Expert Solution & Answer

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Answer 5

Chapter 39, Problem 45P

To determine

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.

Answer 6

Chapter 39, Problem 45P

To determine

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.

Answer 7

Chapter 39, Problem 45P

To determine

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.

Answer 8

Expert Solution & Answer

Answer 9

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Answer 10

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Answer 11

Ch. 39 - Prob. 1Q Ch. 39 - Prob. 2Q Ch. 39 - Prob. 3Q Ch. 39 - Prob. 4Q Ch. 39 - Prob. 5Q Ch. 39 - Prob. 6Q Ch. 39 - Prob. 7Q Ch. 39 - Prob. 8Q Ch. 39 - Prob. 9Q Ch. 39 - Prob. 10Q

a) The radial probability density P ( r ) for ψ 210 . b) The radial probability density P ( r ) for ψ 21 + 1 and ψ 21 - 1 . c) To show that each P ( r ) is consistent with the corresponding dot plot. d) To show that the sum of the radial probability densities is spherically symmetric.

Solution Summary: The author explains that the radial probability density for a real function is the square of the wave function.

Concept explainers

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.

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Chapter 39 Solutions

a) The radial probability density P ( r ) for ψ 210 . b) The radial probability density P ( r ) for ψ 21 + 1 and ψ 21 - 1 . c) To show that each P ( r ) is consistent with the corresponding dot plot. d) To show that the sum of the radial probability densities is spherically symmetric.

Solution Summary: The author explains that the radial probability density for a real function is the square of the wave function.

Concept explainers

To find: a) The radial probability density P(r) for ψ210. b) The radial probability density P(r) for ψ21+1 and ψ21-1. c) To show that each P(r) is consistent with the corresponding dot plot. d) To show that the sum of the radial probability densities is spherically symmetric.

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Chapter 39 Solutions

To find:

a) The radial probability density P(r) for ψ210.

b) The radial probability density P(r) for ψ21+1 and ψ21-1.

c) To show that each P(r) is consistent with the corresponding dot plot.

d) To show that the sum of the radial probability densities is spherically symmetric.