11.1 Time Evolution
Consider again the description of the dynamics of quantum mechanical systems, briefly covered in Chapter 1 (as one of the postulates of quantum mechanics) and Chapter 2 (where we introduced the principles of Adiabatic Quantum Computing). These dynamics are governed by the Schrödinger equation (1.2.2):
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with some initial condition 
, where 
is the quantum state at time t and H is the time-independent Hamiltonian. Its solution is given by (1.2.2), namely
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where the operator U(0,t) is obtained from the Hamiltonian H by (1.2.2):
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We work with units where ℏ is set to 1, so that the system dynamics reads
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If the initial state of the system 
is known, then the state of the system at time t is also known and is determined by the action of the Hamiltonian H over the period of time t.
However, the solution (11.1) assumes that the...
