Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Question
Chapter 10, Problem 10.40E
Interpretation Introduction
Interpretation:
The validation of the statement that Hamiltonian operator is Hermitian is to be explained.
Concept introduction:
According to the Hermitian operator, an operator
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1. Hermitian operators.
Specify (show) which of the following operators are Hermitian: (a) id/dx and (b) id²/dx².
Construct the wavefunction V(r, 0, ø) for an H atoms' electron in the state 2p. Please
note that in order to have a real-valued wavefunction of p, orbital(see below), you need
to do a linear superposition of the corresponding spherical harmonics for the angular
part. Use the spherical harmonics table below. Show that the superposition you selected
indeed results in a real orbital; however, you do not need to simplify the expressions
further or normalize the wavefunction.
y8 = )
Y =
1/2
%3D
Px
3 12
1/2
cos 0
YO = G6)" (5 cos 0-3 cos 0)
%3D
4x
Y1 =7()2 sin Be*io
Y =7(2112 sin 0 (5 cos 6-1)etio
%3D
647)
-y
Yg = G)" (3 cos²0- 1)
Y = " sin? o cos de2i¢
105 1/2
!3!
327
1бл
Y =7
(15 1/2
87
35 12
sin 6e*3i0
1647
sin e cos detie
%3D
%3D
The physical interpretation of the wavefunction and the fact that it is a solution of the Schroedinger equation, which is a 2nd order differential equation, causes many restrictions on an acceptable wave function solution: (i) it must be single-valued; (ii) it must be continuous; (iii) its slope must be continuous; and (iv) it must be normalizable or normalized. Sketch the following functions and check whether they can be wave functions. Explain your answers. (Hint, it might be useful to plot the functions).
Chapter 10 Solutions
Physical Chemistry
Ch. 10 - State the postulates of quantum mechanics...Ch. 10 - Prob. 10.2ECh. 10 - State whether the following functions are...Ch. 10 - State whether the following functions are...Ch. 10 - Prob. 10.5ECh. 10 - Prob. 10.6ECh. 10 - Evaluate the operations in parts a, b, and f in...Ch. 10 - The following operators and functions are defined:...Ch. 10 - Prob. 10.9ECh. 10 - Indicate which of these expressions yield...
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