What is Hermitian, Operator or Eigenfunction?
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What is Hermitian, Operator or Eigenfunction?
by Confusions allowed Mon Sep 12, 2016 6:54 pm
What is considered Hermitian, the operators (x, -i*(h/2π)*d/dx, H^, etc.) or the Wave Function (ψ) itself? Many texts suggest that there are Hermitian Operators, but no one says that the wave function is hermitian.
By the way, a Hermitian operator, as given in various sources, satisfies the property :
(Integral,-inf, inf)fA^g = (Integral,-inf,inf)gA^f, i.e., A^ = A^*.
By the way, a Hermitian operator, as given in various sources, satisfies the property :
(Integral,-inf, inf)fA^g = (Integral,-inf,inf)gA^f, i.e., A^ = A^*.
Confusions allowed- Posts : 15
Join date : 2016-08-04
Age : 25
Re: What is Hermitian, Operator or Eigenfunction?
by manish1012 Mon Sep 12, 2016 10:01 pm
Operators are Hermitian not the wave-function.
A notation:
<ψ₁|O|ψ₂> ≡ ∫ {ψ₁*(O ψ₂)} dx from -∞ to ∞.
There is a quantity called Hermitian Conjugate of any operator
.Let us for the moment denote it as 
.It satisfies
<ψ₁ | O ψ₂> = < ψ₁ | ψ₂>
Now if =
Then is called a Hermitian Operator.
A notation:
<ψ₁|O|ψ₂> ≡ ∫ {ψ₁*(O ψ₂)} dx from -∞ to ∞.
There is a quantity called Hermitian Conjugate of any operator
.Let us for the moment denote it as .It satisfies<ψ₁ | O ψ₂> = <
ψ₁ | ψ₂>Now if
= Then
is called a Hermitian Operator.
manish1012- Posts : 2
Join date : 2016-08-03
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