The role of conjugacy in the dynamics of time of arrival operators
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909285678579712 |
|---|---|
| author | Pablico, Dean Alvin L. Magadan, John Jaykel P. Arguelles, Carl Anthony L. Galapon, Eric A. |
| author_facet | Pablico, Dean Alvin L. Magadan, John Jaykel P. Arguelles, Carl Anthony L. Galapon, Eric A. |
| contents | The construction of time of arrival (TOA) operators canonically conjugate to the system Hamiltonian entails finding the solution of a specific second-order partial differential equation called the time kernel equation (TKE). In this paper, we provide an exact analytic solution of the TKE for a special class of potentials satisfying a specific separability condition. The solution enables us to investigate the time evolution of the eigenfunctions of the conjugacy-preserving TOA operators (CPTOA) and show that they exhibit unitary arrival at the intended arrival point at a time equal to their corresponding eigenvalues. We also compare the dynamics between the TOA operators constructed by quantization and those independent of quantization for specific interaction potentials. We find that the CPTOA operator possesses smoother and sharper unitary dynamics over the Weyl-quantized one within numerical accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The role of conjugacy in the dynamics of time of arrival operators Pablico, Dean Alvin L. Magadan, John Jaykel P. Arguelles, Carl Anthony L. Galapon, Eric A. Quantum Physics The construction of time of arrival (TOA) operators canonically conjugate to the system Hamiltonian entails finding the solution of a specific second-order partial differential equation called the time kernel equation (TKE). In this paper, we provide an exact analytic solution of the TKE for a special class of potentials satisfying a specific separability condition. The solution enables us to investigate the time evolution of the eigenfunctions of the conjugacy-preserving TOA operators (CPTOA) and show that they exhibit unitary arrival at the intended arrival point at a time equal to their corresponding eigenvalues. We also compare the dynamics between the TOA operators constructed by quantization and those independent of quantization for specific interaction potentials. We find that the CPTOA operator possesses smoother and sharper unitary dynamics over the Weyl-quantized one within numerical accuracy. |
| title | The role of conjugacy in the dynamics of time of arrival operators |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.16298 |