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DOE OSTI · 2466197

Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling

May, Michael Q.·Qin, Hong
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Abstract

We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) from the Hamiltonian for two, coupled QHOs and provide a physical picture for the Kravchuk function eigenstates of the oscillator. The familiar $\mathfrak{su}(2)$ structure of the coupled QHO Hamiltonian divides its spectrum into sets corresponding to the DQHO at different resolutions. In addition to energy ladder operators, the formulation allows for the introduction of resolution ladder operators connecting all DQHOs with different resolutions, thus enabling the dynamic scaling of the resolution of finite degree-of-freedom quantum simulations. The coherent state of the DQHO is constructed, and its expected position is proven to oscillate as a classical harmonic oscillator. The DQHO coherent state recovers that of the quantum harmonic oscillator at large resolution.

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97 MATHEMATICS AND COMPUTINGdiscrete quantum harmonic oscillatordynamic resolution adjustmentlie algebrasquantum computationsu(2) oscillator

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May, Michael Q., Qin, Hong. 2024-09-27. Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling. https://doi.org/10.1088/1751-8121%2Fad7ae5

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