Postulate 5: Quantum Mechanics
- Page ID
- 20840
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If a system is in a state described by a wave function \(\psi\), then the average value of the observable corresponding to the \(\hat{A}\) operator is given by
\[ \langle A \rangle = \dfrac{\int_{\infty}^{\infty} \psi^* \hat{A} \psi \;d\tau}{\int_{\infty}^{\infty} \psi^* \psi \;d\tau} \tag{5.1}\]
If the wavefunction is normalizedt, then this expression simplifies to
\[ \langle A \rangle = \int_{\infty}^{\infty} \psi^* \hat{A} \psi \;d\tau \tag{5.2}\]
since
\[\int_{\infty}^{\infty} \psi^* \psi \;d\tau = 1 \tag{5.3}\]