Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Question
Chapter 4.4, Problem 4.30P
(a)
To determine
The normalization constant of the given state.
(b)
To determine
The expectation value of Sx, Sy and Sz.
(c)
To determine
The uncertainties of Sx, Sy and Sz.
(d)
To determine
The results of part (c) are consistent with uncertainty principle or not.
Expert Solution & Answer
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Physics Department
PHYS4101 (Quantum Mechanics)
Assignment 2 (Fall 2020)
Name & ID#.
A three-dimensional harmonic oscillator of mass m has the potential energy
1
1
1
V(x.y.2) = ; mw*x² +mwży² +=mw;z?
where w1 = 2w
a. Write its general eigenvalues and eigenfunctions
b. Determine the eigenvalues and their degeneracies up to the 4th excited state
c. The oscillator is initially equally likely found in the ground, first and second excited states and
is also equally likely found among the states of the degenerate levels. Calculate the expectation
values of the product xyz at time t
b) Explain what the value of the product moment correlation tells you about the relationship between the
daily temperature and the household energy consumption.
4.2. Calculate the results of combining errors when substituting values
in formulae.
1. The length (x) of a rod is measured with with a ruler with an uncertainty of 0.1. Complete
the table for the length of the rod being tripled.
Value
Uncertainty
x/cm
35
0.1
3x/cm
2. The time period of a pendulum is measured by first timing 30 swing. Complete the table to
give the time period and its uncertainty.
Value
Uncertainty
30T/s
75
0.6
T/s
3. You need to find the density of a glass marble. The mass of the marble in grams and the
radius in cm are given in the table below, along with the uncertainty in each measurement.
mass (m)
Using the formula: Density (p).
complete the following table:
%3D
volume (V)
Value
Uncertainty
% uncertainty
Mass (m)/g
4.7
0.2
Radius (r)/cm
0.45
0.01
Volume (V)/cm3
4
(use V =ar³)
3
Density (p)/gcm-1
Chapter 4 Solutions
Introduction To Quantum Mechanics
Ch. 4.1 - Prob. 4.1PCh. 4.1 - Prob. 4.3PCh. 4.1 - Prob. 4.4PCh. 4.1 - Prob. 4.5PCh. 4.1 - Prob. 4.6PCh. 4.1 - Prob. 4.7PCh. 4.1 - Prob. 4.8PCh. 4.1 - Prob. 4.9PCh. 4.1 - Prob. 4.10PCh. 4.1 - Prob. 4.11P
Ch. 4.2 - Prob. 4.12PCh. 4.2 - Prob. 4.13PCh. 4.2 - Prob. 4.14PCh. 4.2 - Prob. 4.15PCh. 4.2 - Prob. 4.16PCh. 4.2 - Prob. 4.17PCh. 4.2 - Prob. 4.18PCh. 4.2 - Prob. 4.19PCh. 4.2 - Prob. 4.20PCh. 4.3 - Prob. 4.21PCh. 4.3 - Prob. 4.22PCh. 4.3 - Prob. 4.23PCh. 4.3 - Prob. 4.24PCh. 4.3 - Prob. 4.25PCh. 4.3 - Prob. 4.26PCh. 4.3 - Prob. 4.27PCh. 4.4 - Prob. 4.28PCh. 4.4 - Prob. 4.29PCh. 4.4 - Prob. 4.30PCh. 4.4 - Prob. 4.31PCh. 4.4 - Prob. 4.32PCh. 4.4 - Prob. 4.33PCh. 4.4 - Prob. 4.34PCh. 4.4 - Prob. 4.35PCh. 4.4 - Prob. 4.36PCh. 4.4 - Prob. 4.37PCh. 4.4 - Prob. 4.38PCh. 4.4 - Prob. 4.39PCh. 4.4 - Prob. 4.40PCh. 4.4 - Prob. 4.41PCh. 4.5 - Prob. 4.42PCh. 4.5 - Prob. 4.43PCh. 4.5 - Prob. 4.44PCh. 4.5 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - Prob. 4.57PCh. 4 - Prob. 4.58PCh. 4 - Prob. 4.59PCh. 4 - Prob. 4.61PCh. 4 - Prob. 4.62PCh. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Prob. 4.65PCh. 4 - Prob. 4.66PCh. 4 - Prob. 4.70PCh. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.75PCh. 4 - Prob. 4.76P
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