Essential University Physics: Volume 2 (3rd Edition)
Essential University Physics: Volume 2 (3rd Edition)
3rd Edition
ISBN: 9780321976420
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 36, Problem 26E
To determine

The energy of the highest energy electron in terms of the ground state energy.

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A particle of mass m is in a harmonic oscillator potential with angular frequency o. It is in the state u(x) = (3u{n=1}(x) + 4u{n=3}(x))/5). a. Give the result of a single measurement of the energy. b. Give the expectation value of the energy. c. Give the expectation value of the momentum. d. Give the result of a single measurement of the momentum. Hint: Average energy is shared equally between the kinetic and potential energy for a simple harmonic oscillator.
6. An electron in hydrogen atom is in initial state Þ(r, 0) = A(2410o + iÞ210 + 421–1 – 2ib211) where wnim are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? hw = - n2 c. Write the state Þ(r, t) at time t, using energy eigenvalues as En d. Find the expectation value of L in the state Þ(r,t e. Find the expectation values of Lx and Ly in the state (r, t f. If measurement of Lz led to the value –ħ what will be results of measurement of energy and the square of total orbital momentum immediately afterwards and what are their probabilities?
An electron is contained in the rectangular box , with widths Lx = 800 pm, Ly =1600 pm, and Lz= 390 pm.What is the electron’s ground-state energy?

Chapter 36 Solutions

Essential University Physics: Volume 2 (3rd Edition)

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