Quantum Time of Arrival

A. Ruschhaupt, Juan Gonzalo Muga, Gerhard C. Hegerfeldt

Denny Lane B. Sombillo, Eric A. Galapon

Eric A. Galapon, Roland Cristopher F. Caballar, Ricardo T. Bahague

We give full account of our recent report in E. A. Galapon, R. Caballar, and R. Bahague, Phys. Rev. Lett. 93, 180406 (2004), where it is shown that formulating the free quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding a complete set of states that evolve to unitarily arrive at a given point at a definite time. For a spatially confined particle, here it is shown explicitly that the problem admits a solution in the form of an eigenvalue problem of a class of compact and self-adjoint time of arrival operators derived by a quantization of the classical time of arrival. The eigenfunctions of these operators are numerically demonstrated to unitarily arrive at the origin at their respective eigenvalues.

I. L. Egusquiza, Juan Gonzalo Muga, Andrés D. Baute

C. K. Raju

Eric A. Galapon, Roland Cristopher F. Caballar, Ricardo T. Bahague

We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For the spatially confined particle, we show that the problem admits a solution in the form of an eigenvalue problem of a compact and self-adjoint time of arrival operator derived by a quantization of the classical time of arrival, which is canonically conjugate with the Hamiltonian in a closed subspace of the Hilbert space.