On a discrete version of the position-momentum commutation relation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914304706478080 |
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| author | Cotfas, Nicolae |
| author_facet | Cotfas, Nicolae |
| contents | The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a discrete version of the position-momentum commutation relation satisfied with approximation of a large part of the pure quantum states. Our purpose is to explore in more details the set of these states. We show that it contains a family of discrete-variable Gaussian states depending on a continuous parameter and certain discrete coherent states. It also contains various discrete-variable versions of the Hermite-Gauss states, defined either as eigenstates of certain discrete versions of the harmonic oscillator Hamiltonian or generated by using a discrete version of the creation or annihilation operator. The presented results suggest a possible way to experimentally obtain some of the investigated states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22753 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a discrete version of the position-momentum commutation relation Cotfas, Nicolae Quantum Physics The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a discrete version of the position-momentum commutation relation satisfied with approximation of a large part of the pure quantum states. Our purpose is to explore in more details the set of these states. We show that it contains a family of discrete-variable Gaussian states depending on a continuous parameter and certain discrete coherent states. It also contains various discrete-variable versions of the Hermite-Gauss states, defined either as eigenstates of certain discrete versions of the harmonic oscillator Hamiltonian or generated by using a discrete version of the creation or annihilation operator. The presented results suggest a possible way to experimentally obtain some of the investigated states. |
| title | On a discrete version of the position-momentum commutation relation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.22753 |