Laplacian operator V² : z +z in spherical polar coordinates is given by ду? az2 1 a a 1 a2 r² sin e ae sin e is an eigenfunction of the Laplacian operator and find the r2. r2 ar %3D r2 sin? e a²¢ sin e sin o Show that function r2 corresponding eigenvalue.
Laplacian operator V² : z +z in spherical polar coordinates is given by ду? az2 1 a a 1 a2 r² sin e ae sin e is an eigenfunction of the Laplacian operator and find the r2. r2 ar %3D r2 sin? e a²¢ sin e sin o Show that function r2 corresponding eigenvalue.
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Transcribed Image Text:a2
Laplacian operator 72 =
ax?
ay? T əz2
in spherical polar coordinates is given by
az?
p² = ()
1 a
1
1
a2
r2 sin e ae sin 0-)
is an eigenfunction of the Laplacian operator and find the
+-
r2 sin 0 a0
r2 ar
ar.
r2 sin? 0 a20
sin 0 sin o
Show that function
r2
corresponding eigenvalue.
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