University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
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Textbook Question
Chapter 7, Problem 65P
Determine the expectation value of the potential energy for a quantum harmonic oscillator in the ground state. Use this to calculate the expectation value of the kinetic energy.
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A quantum mechanical particle of mass m moves in a 1D
potential
where
a) Estimate the ground state energy of the particle.
b) Sketch the wave function to the best of your ability.
Normalize the ground state wave function Ψ0 for the simple harmonic oscillator and find the expectation values (x) and (x 2).
The following Eigen function is a typical solution of the time-independent Schrödinger equation and
satisfies boundary conditions for a particle in a confined space of a certain length.
y(x) = sin
(~77)
(a) Plot the wave function as a function of x for L = 30 cm and n = 1, 2, 3 and 4.
Note: You will need to have 4 plots in the same graph.
(b) On a separate graph, plot the probability density (112) as a function of x using the conditions
specified in part (a). Note: You will need to have 4 plots in the same graph.
(c) Report your observations for parts (a) and (b)
Chapter 7 Solutions
University Physics Volume 3
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