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If a wave function represents knowledge, what does a density matrix mean, then?

I'm curious about this. I've heard of interpretations of quantum theory in which the wave function $\psi$ is taken as representing knowledge, or information (e.g. "Quantum Bayesianism"), about the ...
1
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1answer
386 views

What are pure states and density operators?

I am not sure that I precisely understand what pure states are. It is my understanding that: The principle behind density operators is that the state of a quantum mechanical system is described by ...
2
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2answers
524 views

Quantum states: wave functions or operators

In a typical quantum mechanics course/textbook for physisists, and even in Hall's Quantum Theory for Mathematicians, states of a quantum mechanical system are said to be vectors in some Hilbert space $...
9
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1answer
1k views

Examples of Matrix Product States

Matrix product states (MPS) are a way of representing a (many-body) wavefunction. The method has been described, for example, in The density-matrix renormalization group in the age of matrix ...
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821 views

Superposition and density matrix. What are these states?

I just wanted to understand the following. Let's stay with the harmonic oscillator in QM, just to have an example at hand. First, there are all the different states for $n=1,2,...$. (Let's call them $...
2
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2answers
359 views

Can the wavefunction of a system be reconstructed from density matrices of subsystems?

Suppose we have several interacting particles in pure state $\left|\psi\right>$. For each of particles we can extract density matrices via $$\rho_i(x_i,x_i^\prime)=\int \left<X_i,x_i\middle|\...
4
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9answers
1k views

Does the wave function/density state actually exist?

I have been reading with interest the debates here on whether the wave function/density state actually collapses or not, or whether it is subjective Bayesian or objective with actual complex numbered ...