Changes

<math>Q=\sum_{n}\lambda_n\left|n\right\rangle\left\langle n\right|</math>

<math>Q=\sum_{n}\lambda_n\left|n\right\rangle\left\langle n\right|</math>

The kets may also represent a [[continuous]] set of states.  In such circumstances (which would include, for example, a [[free particle]]), Dirac also found it necessary to develop what is known as the [[Dirac Delta Function]] as an analogue to the [[Kronecker Delta Function]].  For a continuous set of complete kets indexed by the continuous variables <math>x^\prime</math> and <math>x^{\prime\prime}</math>:

The kets may also represent a [[continuous]] set of states.  In such circumstances (which would include, for example, a [[free particle]]), Dirac also found it necessary to develop what is known as the [[Dirac delta]] function as an analogue to the [[Kronecker Delta|Kronecker delta]] function.  For a continuous set of complete kets indexed by the continuous variables <math>x^\prime</math> and <math>x^{\prime\prime}</math>:

<math>\left\langle x^\prime|x^{\prime\prime}\right\rangle = \delta\left(x^\prime-x^{\prime\prime}\right)</math>

<math>\left\langle x^\prime|x^{\prime\prime}\right\rangle = \delta\left(x^\prime-x^{\prime\prime}\right)</math>