1. Some Math: The orbital angular momentum operator in quantum mechanics is defined as a) Using the gradient in spherical coordinates 1 of rde show that V L = -ih(† x V) d dr +e. 1 ô do rsin

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Author:Paul Peter Urone, Roger Hinrichs
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Chapter29: Introduction To Quantum Physics
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Problem 77PE: Integrated Concepts (a) What is for an electron emerging from the Stanford Linear Accelerator with...
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1. Some Math: The orbital angular momentum operator in quantum mechanics is
defined as
a) Using the gradient in spherical coordinates
1 of
r do
show that
V =
b) From part a) show that
ỉ = − iħ(† × V)
d
dr
+
i = -th(c, 20-₁
e
1
rsin
18
sin co
L₂ = ẹ₂
· Ī =— iħ-
e.
c) Find the eigenfunctions of L₂ given in part b)
ə
ap
ô
do
Transcribed Image Text:1. Some Math: The orbital angular momentum operator in quantum mechanics is defined as a) Using the gradient in spherical coordinates 1 of r do show that V = b) From part a) show that ỉ = − iħ(† × V) d dr + i = -th(c, 20-₁ e 1 rsin 18 sin co L₂ = ẹ₂ · Ī =— iħ- e. c) Find the eigenfunctions of L₂ given in part b) ə ap ô do
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