- #1

patric44

- 296

- 39

- Homework Statement
- prove that : <A^n>=<A>^n

- Relevant Equations
- <A^n>=<A>^n

hi all

how do I prove that

$$

<A^{n}>=<A>^{n}

$$

It seems intuitive but how do I rigorously prove it, My attempt was like , the LHS can be written as:

$$

\bra{\Psi}\hat{A}.\hat{A}.\hat{A}...\ket{\Psi}=\lambda^{n} \bra{\Psi}\ket{\Psi}=\lambda^{n}\delta_{ii}=\lambda^{n}

$$

and the RHS equal:

$$

<A>^{n}=[\bra{\Psi}A\ket{\Psi}]^{n}=\lambda^{n}[\bra{\Psi}\ket{\Psi}]^{n}=\lambda^{n}[\delta_{ii}]^{n}=\lambda^{n}

$$

Is my proof rigurus enough or there are other formal proof for that

how do I prove that

$$

<A^{n}>=<A>^{n}

$$

It seems intuitive but how do I rigorously prove it, My attempt was like , the LHS can be written as:

$$

\bra{\Psi}\hat{A}.\hat{A}.\hat{A}...\ket{\Psi}=\lambda^{n} \bra{\Psi}\ket{\Psi}=\lambda^{n}\delta_{ii}=\lambda^{n}

$$

and the RHS equal:

$$

<A>^{n}=[\bra{\Psi}A\ket{\Psi}]^{n}=\lambda^{n}[\bra{\Psi}\ket{\Psi}]^{n}=\lambda^{n}[\delta_{ii}]^{n}=\lambda^{n}

$$

Is my proof rigurus enough or there are other formal proof for that