Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 3.5, Problem 3.15P
To determine
To prove the relation
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PROVE: Triangle Inequality We prove Property 5 of abso-
lute values, the Triangle Inequality:
|x + y < |x| + y|
(a) Verify that the Triangle Inequality holds for x = 2 and
y = 3, for x = -2 and y = -3, and for x = -2 and
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(b) Prove that the Triangle Inequality is true for all real num-
bers x and y. [Hint: Take cases.]
Consider the function
v(1,2) =(
[1s(1) 3s(2) + 3s(1) 1s(2)]
[x(1) B(2) + B(1) a(2)]
Which of the following statements is incorrect concerning p(1,2) ?
a.
W(1,2) is normalized.
Ob.
The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons.
OC.
y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with
eigenvalue = -5 hartree.
d.
The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit.
Oe.
The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.
Consider the wave function for the ground state harmonic oscillator:
m w1/4
e-m w x2/(2 h)
A. What is the quantum number for this ground state? v = 0
B. Enter the integrand you'd need to evaluate (x) for the ground state harmonic oscillator wave 'function: (x) = |-
то
dx
e
C. Evaluate the integral in part B. What do you obtain for the average displacement? 0
Chapter 3 Solutions
Introduction To Quantum Mechanics
Ch. 3.1 - Prob. 3.1PCh. 3.1 - Prob. 3.2PCh. 3.2 - Prob. 3.3PCh. 3.2 - Prob. 3.4PCh. 3.2 - Prob. 3.5PCh. 3.2 - Prob. 3.6PCh. 3.3 - Prob. 3.7PCh. 3.3 - Prob. 3.8PCh. 3.3 - Prob. 3.9PCh. 3.3 - Prob. 3.10P
Ch. 3.4 - Prob. 3.11PCh. 3.4 - Prob. 3.12PCh. 3.4 - Prob. 3.13PCh. 3.5 - Prob. 3.14PCh. 3.5 - Prob. 3.15PCh. 3.5 - Prob. 3.16PCh. 3.5 - Prob. 3.17PCh. 3.5 - Prob. 3.18PCh. 3.5 - Prob. 3.19PCh. 3.5 - Prob. 3.20PCh. 3.5 - Prob. 3.21PCh. 3.5 - Prob. 3.22PCh. 3.6 - Prob. 3.23PCh. 3.6 - Prob. 3.24PCh. 3.6 - Prob. 3.25PCh. 3.6 - Prob. 3.26PCh. 3.6 - Prob. 3.27PCh. 3.6 - Prob. 3.28PCh. 3.6 - Prob. 3.29PCh. 3.6 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48P
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