Lagrangian Formulation of Quantum Mechanics

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SUMMARY

The discussion centers on the Lagrangian formulation of Quantum Mechanics (QM) and Quantum Field Theory (QFT). It establishes that while textbooks on QFT often present Lagrangians, there is no comprehensive Lagrangian approach applicable to QM or QFT. The conversation highlights the distinction between the path integral formulation and the canonical operator approach, emphasizing that the path integral is not a true Lagrangian formulation but shares similarities. For further reference, a specific resource is provided: a PDF from the University of Illinois on Quantum Mechanics.

PREREQUISITES
  • Understanding of Quantum Mechanics principles
  • Familiarity with Quantum Field Theory concepts
  • Knowledge of Lagrangian mechanics
  • Basic grasp of path integral formulation
NEXT STEPS
  • Explore textbooks on Quantum Field Theory for Lagrangian examples
  • Study the path integral formulation of Quantum Mechanics
  • Research the canonical operator approach in Quantum Mechanics
  • Review the provided PDF resource for detailed insights on Quantum Mechanics
USEFUL FOR

Students of physics, theoretical physicists, and researchers interested in the foundations of Quantum Mechanics and Quantum Field Theory.

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Which textbooks formulate Quantum Mechanics (or, for that matter, QFT) in Langrangian terms?
 
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You can define the action of a QFT in terms of a Lagrangian, but there is no equivalent Lagrangian approach that works in QFT or QM. It's simply not how quantum theory works. You either have the path integral approach or the canonical (operator) approach.

If you just want to look up what the Lagrangians look like: pretty much any book on QFT will treat these.
 

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