Let (0) and ø(0) be arbitrary functions of the angle 0 which have the property b(0) = v(0 + 27) and ø(0) = ø(0 + 27), since the angles 0 and 0 + 2n are physically %3D identical. Show that the operator ÔN = i (8/d0)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let (0) and ø(0) be arbitrary functions of the angle 0 which have the property
(0) = v(0 + 2n) and ø(0) = ¢(0 + 2n), since the angles 0 and 0 + 2n are physically
identical. Show that the operator
ÔN = i (0/d0)
is Hermitian if 0 spans the angular range from 0 to 27 radians.
Hint: Calculate the integral
do o*(0) Ñ v(0)
by parts to show that
r27
2T
do 4* (0) ÔÑ 4(Ð) = |.
d0 [ÎÑ ø(0)]* v(0) .
Transcribed Image Text:Let (0) and ø(0) be arbitrary functions of the angle 0 which have the property (0) = v(0 + 2n) and ø(0) = ¢(0 + 2n), since the angles 0 and 0 + 2n are physically identical. Show that the operator ÔN = i (0/d0) is Hermitian if 0 spans the angular range from 0 to 27 radians. Hint: Calculate the integral do o*(0) Ñ v(0) by parts to show that r27 2T do 4* (0) ÔÑ 4(Ð) = |. d0 [ÎÑ ø(0)]* v(0) .
Expert Solution
Step 1

Given,

ψθ=ψθ+2πϕθ=ϕθ+2π

To, show Ω^=iθ is Hermitian.

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