# What is Hermitian, Operator or Eigenfunction?

## What is Hermitian, Operator or Eigenfunction?

What is considered Hermitian, the operators (x, -i*(h/2π)*d/dx, H

By the way, a Hermitian operator, as given in various sources, satisfies the property :

(Integral,-inf, inf)fA

^{^}, 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^{^}^{*}.**Confusions allowed**- Posts : 15

Join date : 2016-08-04

Age : 19

## Re: What is Hermitian, Operator or Eigenfunction?

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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