mathematical methods for scientists and … art/chapter 16/chapter16_27to38.pdffor the novice...
TRANSCRIPT
Chapter 16 Figures 27 To 38 From
MATHEMATICAL METHODS
for Scientists and Engineers
Donald A. McQuarrie
For the Novice Acrobat User or the Forgetful
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ANIMATIONS
Figures 16.30, 16.32, 16.34, and 16.35 each has an associated animation that requires QuickTime™ for display. The names of the animation files are Anim16_30.mov, Anim16_32.mov, Anim16_34.mov, and Anim16_35.mov, respectively. Each of the animations must be independently downloaded from the server.
x
y
z
l
Figure 16.27 A slab of uniform material of thickness l.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
xl
Figure 16.28A thin homogeneous wire of length l that is insulated along its lateral surface so that the temperature varies only in the x direction.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
t t
x
T = 0T = 0
f HxL
0 1
Figure 16.29 A summary of the boundary coditions and the initial conditions for Equations 1 and 2.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
T
xêl
Figure 16.30 The solution to the equations in Example 1 plotted against x for several values of t = a2p2t / l2.
a2p2t / l2
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
x
Tx=
0
Tx=
0
T0 sin2pxêl
0 l
t t
Figure 16.31 A summary of the boundary conditions and the initial condition for Example 2.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
a2 tê l
T
xêl
Figure 16.32 The solutions to the equations in Example 2 plotted against x/l for various values of t = 4p2kt/l2.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
x
hTHl,tL+TxHl,tL=
0
T=
0T0
0 l
t t
Figure 16.33 A summary of the boundary conditions and the initial condition for Example 3.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
a2 t
T
xêl
Figure 16.34 The solution in Example 3 plotted against x for various values of a2t for h = l = 1.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
x
T
Figure 16.35The time evolution of the solution given in Example 4, showing how T(x, t) aproaches the steady-state solution s(x) = 1 + x (white).
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
x
y
z
ab
c
Figure 16.36A rectangular parallelepiped of sides a, b, and c. In the quantum-mechanical problem of a particle in a box, the particle is restricted to lie within a potential-free parallelepiped.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
nx2+ny2+nz2
0
3
6
9
1112
14
171819
Hnx , n y , n z L
H111 L
H211 L H121 L H112 L
H221 L H212 L H122 L
H311 L H131 L H113 LH222 L
H321 L H312 L H231 L
H132 L H123 L H213 L
H322 L H232 L H223 LH411 L H141 L H114 LH331 L H313 L H133 L
Figure 16.37 The allowed energy levels for a particle in a box with a = b = c.
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books
x
y
z
q
f
Figure 16.38The model of a rigid rotator. We can choose our coordinate system so that one of the masses sits at the origin and the other takes on a reduced mass m = m1m2/(m1 + m2).
From MATHEMATICAL METHODS for Scientists and Engineers, Donald A. McQuarrie, Copyright 2003 University Science Books