A one-particle time of arrival operator for a free relativistic spin-0 charged particle in (1+1) dimensions

作者：Bunao Joseph; Galapon Eric A^*

来源：Annals of Physics, 2015, 353: 83-106.

DOI：10.1016/j.aop.2014.11.003

• Quantum arrival time
• Spin-0
• Klein-Gordon particle

We construct a one-particle TOA operator (T) over cap canonically conjugate with the Hamiltonian describing a free, charged, spin-0, relativistic particle in one spatial dimension and show that it is maximally symmetric. We solve for its eigenfunctions and show that they form a complete and non-orthogonal set. Plotting the time evolution of their corresponding probability densities, it implies that the eigenfunctions become more localized at the origin at the time equal to their eigenvalues. That is, a particle being described by an eigenfunction of (T) over cap is in a state of definite arrival time at the origin and at the corresponding eigenvalue. We also calculate the TOA probability distribution of a particle in some initial state.

• 出版日期2015-2