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Time Evolution in Quantum Mechanics

Chapter 15 Time Evolution in Quantum MechanicsPhysicalsystems are, in general, dynamical, they evolve in time. The dynamics of classicalmechanical systems are described by Newton s laws of motion, while the dynamics of theclassical electromagnetic field is determined by Maxwell s equations. Either Newton s equationsor Maxwell s equations constitute laws of physics whose form is particular to the kind of systemthat is being described, though some unification is provided in terms of Hamilton s principle, auniversal way of stating the laws of classical dynamics. What we require is a means by which thedynamical properties of Quantum systems can be described, given the state| (0) of a quantumsystem at some initial timet=0, what is required is a physical law that tells us what the state willbe at some other timet, a Quantum law of Evolution .

In contrast, if the system were open, i.e. not isolated, then there is the prospect of time dependent external influences acting on the system – e.g. an externally produced laser pulse fired at an atom – so the evolution of the ... momentum p, for which the wave function is …

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