Solving the Schrödinger equation by reduction to a first-order differential operator through a coherent states transform |
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Institution: | School of Mathematics, University of Leeds, Leeds LS2 9JT, UK |
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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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Keywords: | Coherent states Airy beam Schrödinger equation Magnetic field |
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