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arXiv · 1903.03554

Solving the Schrodinger Equation by Reduction to a First-order Differential Operator through a Coherent States Transform

Fadhel Almalki·Vladimir V. Kisil
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Abstract

The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to first-order partial differential operators. Therefore, the respective dynamics can be explicitly solved through a flow of points in extensions of the phase space. This generalises the geometric dynamics of a harmonic oscillator in the Fock space. We describe all Hamiltonians which are geometrised (in the above sense) by Gaussian and Airy beams and write down explicit solutions for such systems.

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Fadhel Almalki, Vladimir V. Kisil. 2019-03-08. Solving the Schrodinger Equation by Reduction to a First-order Differential Operator through a Coherent States Transform. https://doi.org/10.1016/j.physleta.2020.126330

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