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Expectation value of the square of the observable

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Homework Statement


I know how to compute the expectation value of an observable. But how does one compute the expectation value of an observable's square?

Homework Equations


[tex]\langle Q \rangle = \int_{-\infty}^{\infty} \Psi^* \hat{Q} \Psi \; dx[/tex]
[tex]\langle Q^2 \rangle = \int_{-\infty}^{\infty} \Psi^* (\hat{Q} \Psi)^2 \; dx \; ???[/tex]
 
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Answers and Replies

  • #2
dextercioby
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No, the square is defined by double application of the operator

[tex] A^2 \psi =A\left(A \psi \right) \ , \forall \psi\in D(A) \ \mbox{and} \ {} A\psi \in D(A)[/tex]
 
  • #3
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I tried double application after I posted and got more elegant answers. Thanks dextercioby.
 

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