Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 6.2, Problem 6.5P
To determine

Show that the equation ψ(x)=eiqxu(x) follows from ψ(xa)=eiqaψ(x), and also show that u(x) is a periodic function.

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A object of mass 3.00 kg is subject to a force FX that varies with position as in the figure below. Fx (N) 4 3 2 1 x(m) 2 4 6 8 10 12 14 16 18 20 i (a) Find the work done by the force on the object as it moves from x = 0 to x = 5.00 m. J (b) Find the work done by the force on the object as it moves from x = 5.00 m to x = 11.0 m. ] (c) Find the work done by the force on the object as it moves from x = 11.0 m to x = 18.0 m. J (d) If the object has a speed of 0.400 m/s at x = 0, find its speed at x = 5.00 m and its speed at x speed at x = 5.00 m speed at x = 18.0 m m/s m/s = 18.0 m.
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A child's pogo stick (figure below) stores energy in a spring (k = 2.05 × 104 N/m). At position (✗₁ = -0.100 m), the spring compression is a maximum and the child is momentarily at rest. At position ® (x = 0), the spring is relaxed and the child is moving upward. At position child is again momentarily at rest at the top of the jump. Assume that the combined mass of child and pogo stick is 20.0 kg. B A (a) Calculate the total energy of the system if both potential energies are zero at x = 0. (b) Determine X2- m (c) Calculate the speed of the child at x = 0. m/s (d) Determine the value of x for which the kinetic energy of the system is a maximum. mm (e) Obtain the child's maximum upward speed. m/s the
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