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Quantum dynamics guided by Hamilton's principal function.

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Title: Quantum dynamics guided by Hamilton's principal function.
Authors: Campos, Diógenes1 (AUTHOR) dcamposr@unal.edu.co
Source: Pramana: Journal of Physics. Jun2026, Vol. 100 Issue 2, p1-14. 14p.
Subjects: Hamilton's principle function, Hamilton-Jacobi equations, Quantum theory, Trajectories (Mechanics), Schrödinger equation, Quantization methods (Quantum mechanics), Electromagnetic fields, Quantum transitions
Abstract: To address systems with spatially and temporally varying particle masses, we construct the Hamiltonian using Born-Jordan quantisation. This approach also includes systems influenced by electromagnetic fields as a specific case. By introducing a transformation based on a freely chosen action function, we can separate the time-dependent Schrödinger equation into two distinct components: the classical Hamilton–Jacobi equation and a complementary quantum term. The classical part yields Hamilton's principal function, which, when promoted to an operator, governs the quantum dynamics. Ultimately, by applying established methods from quantum mechanics, we investigate the relationship between quantum and classical dynamics. We particularly emphasise the role of classical trajectories, mediated through Hamilton's principal function, in shaping quantum behaviour. [ABSTRACT FROM AUTHOR]
Copyright of Pramana: Journal of Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: To address systems with spatially and temporally varying particle masses, we construct the Hamiltonian using Born-Jordan quantisation. This approach also includes systems influenced by electromagnetic fields as a specific case. By introducing a transformation based on a freely chosen action function, we can separate the time-dependent Schrödinger equation into two distinct components: the classical Hamilton–Jacobi equation and a complementary quantum term. The classical part yields Hamilton's principal function, which, when promoted to an operator, governs the quantum dynamics. Ultimately, by applying established methods from quantum mechanics, we investigate the relationship between quantum and classical dynamics. We particularly emphasise the role of classical trajectories, mediated through Hamilton's principal function, in shaping quantum behaviour. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Pramana: Journal of Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s12043-025-03089-x
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      – Code: eng
        Text: English
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        PageCount: 14
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      – SubjectFull: Hamilton's principle function
        Type: general
      – SubjectFull: Hamilton-Jacobi equations
        Type: general
      – SubjectFull: Quantum theory
        Type: general
      – SubjectFull: Trajectories (Mechanics)
        Type: general
      – SubjectFull: Schrödinger equation
        Type: general
      – SubjectFull: Quantization methods (Quantum mechanics)
        Type: general
      – SubjectFull: Electromagnetic fields
        Type: general
      – SubjectFull: Quantum transitions
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              Text: Jun2026
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              Y: 2026
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