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- Summary
- Can mixed states be seen as many particles and formulas

Considering a mixture ##\sum p_i|\Psi_i\rangle\langle\Psi_i|##

This does not describe an ensemble of quantum systems since the particle number is defined by ##\Psi_i##.

The question is in the continuous wave-mechanical formalism where I don't understand what object the density matrix is : I know ##\langle\Psi_i|x\rangle=\Psi_i(x)=\int \Psi_i(x')\delta(x-x')dx'##. It seems that here I could exchange the order but what happen to the braces ? Is it ##|\Psi_i\rangle\langle\Psi_i|=\Psi_i(x)\int\Psi_i(x')\delta(x'-x'')[\circ]dx'## ?

Where ##\circ## means it's the place for a function in ##x''## ?

Why is then the sum different than a single term ?

This does not describe an ensemble of quantum systems since the particle number is defined by ##\Psi_i##.

The question is in the continuous wave-mechanical formalism where I don't understand what object the density matrix is : I know ##\langle\Psi_i|x\rangle=\Psi_i(x)=\int \Psi_i(x')\delta(x-x')dx'##. It seems that here I could exchange the order but what happen to the braces ? Is it ##|\Psi_i\rangle\langle\Psi_i|=\Psi_i(x)\int\Psi_i(x')\delta(x'-x'')[\circ]dx'## ?

Where ##\circ## means it's the place for a function in ##x''## ?

Why is then the sum different than a single term ?