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Models are idealizations of physical reality involve a particular structure or pattern. Models can be mathematical, logical, pictoral, or a physical object (but not usually in physics). Models only approximate reality; they represent an idealization of reality (e.g. with no friction, ignore bending of rigid bodies, etc.), but generally they are applicable to many situations (else the model is not useful). Models generally involve a cluster of several concepts and theories (e.g. harmonic motion involves kinematics, F=ma, and a linear restoring force). Models almost always may be expressed in several representations, and the cross connection of these representations provides a richness for the models. For example, motion with constant acceleration may be represented with standard equations, strobe pictures of the object, graphs or tables of kinematic variables vs. time, or a concise verbal description. The two level system may be represented using the equations following from time-dependent perturbation theory, the Bloch vector, and the density matrix.
Physicists and educational psychologists agree that understanding a model implies fluency with, and ability to transfer between, all of its commonly used representations. A physicist familiar with any model can recognize/describe/understand/quantitatively predict situations that fit within the model's assumptions with little effort (as an exercise), but is typically confronted with a "problem" if even a small discrepancy exists between the situation at hand and the relevant model.
Being able to understand and use a model involves:
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