Is there a guide to using the density matrix formalism in quantum mechanics?

peterjaybee
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Hello, I am looking for a guide to quantum mechanics and the density matrix formalism which uses the Einstein summation convention. Does such a guide exist?
 
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I ask because bra's and ket's seem to behave in a similar manner to co-varient and contra-varient vectors. I guess this is not a coincidence.
 
peterjaybee said:
I ask because bra's and ket's seem to behave in a similar manner to co-varient and contra-varient vectors. I guess this is not a coincidence.

No. See the section ''What are bras and kets'' in Chapter A1 of my theoretical physics FAQ at
http://arnold-neumaier.at/physfaq/physics-faq.html#A1
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

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