Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling

Journal Article · 27 September 2024 · Journal of Physics. A, Mathematical and Theoretical

DOI: https://doi.org/10.1088/1751-8121/ad7ae5 · OSTI ID:2466197

May, Michael Q.  ^[1]; Qin, Hong  ^[1]

---

1. Princeton University, NJ (United States). Princeton Plasma Physics Laboratory (PPPL)

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.

• Research Organization: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-09CH11466
• OSTI ID: 2466197
• Journal Information: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 41 Vol. 57; ISSN 1751-8113
• Publisher: IOP PublishingCopyright Statement
• Country of Publication: United States
• Language: English