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Added stuff about probability
Other examples include energy and time, as well as different components of [[angular momentum]].
Other examples include energy and time, as well as different components of [[angular momentum]].
===Probability===
The probability a particle is found in a certain region <math>a < x < b</math> can be described as:
<math>
p(a < x < b) = \int^b_a |\Psi (x,t)|^2 dx
</math>
provided that the wavefunction is normalised:
<math>
\int^\infty_{-\infty} |\Psi (x,t)|^2 dx = 1
</math>
In general, the expected value of a measurement of a quantity <math>Q</math> can be described as:
<math>
\langle Q \rangle = \int^\infty_{-\infty} \Psi^{*} \hat{Q} \, \Psi dx
</math>
where <math>\hat{Q}</math> is the [[operator]] associated with the quantity <math>Q</math>. For example the position operator is simply <math>x</math>. The [[momentum (physics)|momentum]] operator is:
<math>\hat{p} = \frac{\hbar}{i} \frac{\partial}{\partial x}</math>
so that the expected momentum is:
<math>\langle p \rangle = \int^\infty_{-\infty} \Psi^{*} \hat{p} \, \Psi dx = \frac{\hbar}{i} \int^\infty_{-\infty} \Psi^{*} \frac{\partial \Psi}{\partial x} dx
==Interpretations==
==Interpretations==