Time-evolution of an observer means how it changes over time; it's derivative over time. In quantum mechanics, it is described by the Hamiltonian. DO NOT use this tag for evolving laws of physics.

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Hamiltonian mechanics and conservation of energy?

Can anyone explain to me Hamiltonian mechanics relation to conservation of energy? I'm not very good at mathematics, and I know it's important into understanding Hamiltonian mechanics. However, can ...
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Question about equation 2.27 from Pachos's Introduction to topological quantum computing

http://quince.leeds.ac.uk/~phyjkp/Files/IntroTQC.pdf above is the PDF that is hosted on his website. The equation is on page 22 (pg 30 in the pdf). In chapter 2. It is the second equation of the ...
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Time Evolution Operator in Interaction Picture (Harmonic Oscillator with Time Dependent Perturbation)

1. The problem statement, all variables and given/known data Consider a time-dependent harmonic oscillator with Hamiltonian $$\hat{H}(t)=\hat{H}_0+\hat{V}(t)$$ $$\hat{H}_0=\hbar \omega \left( ...
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Time evolution of quantum states

Time evolution of a quantum state is fully described by a one parameter family of unitary operators. What I can't seem to understand is, given some unitary operator acting on some Hilbert space, can ...