The Hamilton-Jacobi Equation : an intuitive approach

The Hamilton-Jacobi equation (HJE) is one of the most elegant approach to Lagrangian systems such as geometrical optics and classical mechanics, establishing the duality between trajectories and waves and paving the way naturally for the quantum mechanics. Usually, this formalism is taught at the en...

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Bibliographic Details
Published inAmerican journal of physics Vol. 88; no. 5; pp. 353 - 359
Main Author Houchmandzadeh, Bahram
Format Journal Article
LanguageEnglish
Published American Association of Physics Teachers 21.04.2020
Subjects
Classical Physics
Physics
Action
Lagrangian
Wave-trajectory duality
Hamiltonian
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ISSN0002-9505
1943-2909

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Summary:The Hamilton-Jacobi equation (HJE) is one of the most elegant approach to Lagrangian systems such as geometrical optics and classical mechanics, establishing the duality between trajectories and waves and paving the way naturally for the quantum mechanics. Usually, this formalism is taught at the end of a course on analytical mechanics through its technical aspects and its relation to canonical transformations. I propose that the teaching of this subject be centered on this duality along the lines proposed here, and the canonical transformations be taught only after some familiarity with the HJE has been gained by the students.
ISSN:0002-9505
1943-2909