Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 1.5, Problem 1.6P
To determine
The reason why it is impossible to do integration by parts in the middle of the equation 1.29.
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(a) Find the scalar products î · î, ĵ· ĵ, and k · Ê.
(b) Find î · ĵ, ĵ · k, and k · î
(c) Use the distributive law to multiply out the scalar product of two arbitrary vectors Ã
Axî + Ayî + A¸k and B
Equation 6.4.
Bxî + Byĵ + Bzk, and use the results of (a) and (b) to verify
Consider a rectangular surface of length L and width W in the xy plane with its center at the origin:
Which of the following are valid expressions for the area vector of this surface? Check all that apply.
O (0,0, LW)
O (W, L, 0)
O (0,0, -LW)
O (LW, LW, 0)
O (0, LW, 0)
O (L, W, 0)
Problems
5.1 Determine the material derivative of the flux of any vector property
Qj through the spatial area S. Specifically, show that
in agreement with Eq 5.2-5.
1999 by CRC Press LLC
5.2 Let the property P in Eq 5.2-1 be the scalar 1 so that the integral in
that equation represents the instantaneous volume V. Show that in
this case
dV =
5.3 Verify the identity
!!
and, by using this identity as well as the result of Problem 5.1, prove
that the material derivative of the vorticity flux equals one half the
flux of the curl of the acceleration; that is, show that
5.4 Making use of the divergence theorem of Gauss together with the
identity
aw
at
show that
w,v, -
dt
Chapter 1 Solutions
Introduction To Quantum Mechanics
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