I am familiar with the derivation of the resolution of the identity proof in Dirac notation. Where ## | \psi \rangle ## can be represented as a linear combination of basis vectors ## | n \rangle ## such that:(adsbygoogle = window.adsbygoogle || []).push({});

## | \psi \rangle = \sum_{n} c_n | n \rangle = \sum_{n} | n \rangle c_n ##

Assuming an orthonormal basis, then:

## c_n = \langle n | \psi \rangle ##

Such that:

## | \psi \rangle = \sum_{n} | n \rangle \langle n | \psi \rangle ##

Thus:

## 1 = \sum_{n} | n \rangle \langle n | ##

However, I don't think that I understand the derivation well in enough to derive it without using Dirac notation. Does anyone know a proof of the identity without using Dirac notation, both for discrete and continuous variables?

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# I Deriving resolution of the identity without Dirac notation

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