Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ ( x , t ) = Ψ ( x , 0 ) .

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Answer 1

Question

Chapter 2, Problem 2.38P

(a)

To determine

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ(x,t)=Ψ(x,0).

(b)

To determine

The revival time, for a particle of energy bouncing back and forth between the walls.

(c)

To determine

Show that the energy of the two revival times equals.

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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).

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simple diagram to illustrate the setup for each law- coulombs law and biot savart law

Answer 2

Question

Chapter 2, Problem 2.38P

(a)

To determine

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ(x,t)=Ψ(x,0).

(b)

To determine

The revival time, for a particle of energy bouncing back and forth between the walls.

(c)

To determine

Show that the energy of the two revival times equals.

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Answer 3

Question

Chapter 2, Problem 2.38P

(a)

To determine

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ(x,t)=Ψ(x,0).

(b)

To determine

The revival time, for a particle of energy bouncing back and forth between the walls.

(c)

To determine

Show that the energy of the two revival times equals.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2, Problem 2.38P

(a)

To determine

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ(x,t)=Ψ(x,0).

(b)

To determine

The revival time, for a particle of energy bouncing back and forth between the walls.

(c)

To determine

Show that the energy of the two revival times equals.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 2, Problem 2.38P

(a)

To determine

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ(x,t)=Ψ(x,0).

(b)

To determine

The revival time, for a particle of energy bouncing back and forth between the walls.

(c)

To determine

Show that the energy of the two revival times equals.

Answer 6

Chapter 2, Problem 2.38P

(a)

To determine

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ(x,t)=Ψ(x,0).

Answer 7

Chapter 2, Problem 2.38P

(a)

To determine

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ(x,t)=Ψ(x,0).

Answer 8

(b)

To determine

The revival time, for a particle of energy bouncing back and forth between the walls.

Answer 9

(b)

To determine

The revival time, for a particle of energy bouncing back and forth between the walls.

Answer 10

(c)

To determine

Show that the energy of the two revival times equals.

Answer 11

(c)

To determine

Show that the energy of the two revival times equals.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 2.1 - Prob. 2.1P Ch. 2.1 - Prob. 2.2P Ch. 2.2 - Prob. 2.3P Ch. 2.2 - Prob. 2.4P Ch. 2.2 - Prob. 2.5P Ch. 2.2 - Prob. 2.6P Ch. 2.2 - Prob. 2.7P Ch. 2.2 - Prob. 2.8P Ch. 2.2 - Prob. 2.9P Ch. 2.3 - Prob. 2.10P

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ ( x , t ) = Ψ ( x , 0 ) .

Solution Summary: The author explains that the wave function of a particle in the infinite square well returns to its original form after quantum revival time.

Concept explainers

Show that the wave function of a particle in the infinite square well returns to its original form after quantum revival time Ψ(x,t)=Ψ(x,0).

The revival time, for a particle of energy bouncing back and forth between the walls.

Show that the energy of the two revival times equals.

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Chapter 2 Solutions