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Lecture6.QM.to.Lagrangian.Densities

Lecture6.QM.to.Lagrangian.Densities - Lagrangian Densities...

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F Q M h i From Quantum Mechanics to Lagrangian Densities Just as there is no “derivation” of quantum mechanics from classical mechanics, there is no derivation of relativistic field theory from quantum mechanics. The “route” from one to the other is based on physically route from one to the other is based on reasonable postulates and the imposition of Lorentz invariance and relativistic kinematics . The final “theory” is a model whose survival depends absolutely on its success in producing “numbers” which agree with experiment.
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Summary: Quantum Mechanics The ten minute course in QM. Momentum Becomes an operator and use The Hamiltonian becomes an operator.
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Physical interpretation of the wave function. This condition places a strong mathematical condition on the wave function.
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N h h S h di Note that the Schrodinger equation reflects this relationship
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Quantization arises from placing boundary conditions on the wave function. It is a mathematical result!
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A “toy” model postulate approach to quantum field theory A toy model postulate approach to quantum field theory
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Note that * ( r ,t) ( r ,t) does not represent the probability per unit volume density of the particle being at ( r ,t).
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The resulting “wave equation”:
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