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)
A pendulum of length l and mass m is mounted on a block of mass M. The block can movefreely without friction on a horizontal surface as shown in Fig 1
PHYS 24021. Consider a particle of mass m moving in a plane under the attractive force μm/r2 directedto the origin of polar coordinates r, θ. Determine the equations of motion.2. Write down the Lagrangian for a simple pendulum constrained to move in a single verticalplane. Find from it the equation of motion and show that for small displacements fromequilibrium the pendulum performs simple harmonic motion.3. A pendulum of length l and mass m is mounted on a block of mass M. The block can movefreely without friction on a horizontal surface as shown in Fig 1.Figure 1Show that the Lagrangian for the system isL =( M + m2)( ̇x)2 + ml ̇x ̇θ + m2 l2( ̇θ)2 + mgl(1 − θ22)
Chapter 1 Solutions
Introduction To Quantum Mechanics
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- Problem 5.25 If B is uniform, show that A(r) = - (r x B) works. That is, check that V · A = 0 and V × A = B. Is this result unique, or are there other functions with the same divergence and curl?arrow_forwardHow is it that I can have b=x in problem 7.48?arrow_forwardA triangle in the xy plane is defined with corners at (x, y) = (0,0), (0, 2) and (4, 2). We want to integrate some function f(x, y) over the interior of this triangle. Choosing dx as the inner integral, the required expression to integrate is given by: Select one: o Sro S-o f(x, y) dx dy x=0 2y y=0 O S-o So F(x, y) dæ dy O o S f(x, y) dy dæ O So So F(x, y) dx dy x/2 =0arrow_forward
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