Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 10.2, Problem 10.3P
To determine
Prove Equation 10.33, starting with Equation 10.32.
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A point particle moves in space under the influence of a force derivablefrom a generalized potential of the formU(r, v) = V (r) + σ · L,where r is the radius vector from a fixed point, L is the angular momentumabout that point, and σ is the fixed vector in space.
Find the components of the force on the particle in spherical polar coordinates, on the basis of the equation for the components of the generalized force Qj:
Qj = −∂U/∂qj + d/dt (∂U/∂q˙j)
What does your result for the potential energy U(x=+L) become in the limit a→0?
Let f(x)= 4xex - sin(5x). Find the third derivative of this function.
Note ex is denoted as e^x below.
Select one:
(12+4x^3)e^x + 125sin(5x)
12e^x + 125cos(5x)
not in the list
(12+4x)e^x + 125cos(5x)
(8+4x)e^x + 25sin(5x)
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