Quantizations of the classical time of arrival and their dynamics

Abstract

The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of two variable polynomial functions. This leads to representations of the quantized time of arrival operators as integral operators whose kernels are determined by the chosen ordering rule. The formulation lends itself to generalization which allows construction of time of arrival operators that cannot be obtained by direct quantization using particular ordering rules. Wey, symmetric and Born-Jordan quantizations are specifically studied. The dynamics of the eigenfunctions of the different time of arrival operators are investigated. The eigenfunctions exhibit unitary arrival at the intended arrival point at their respective eigenvalues.

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Cited by in corpus (9)

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• The time distribution of quantum events
• Relativistic free motion time of arrival operator for massive spin-0 particles with positive energy
• Conjugates to One Particle Hamiltonians in 1-Dimension in Differential Form
• The role of conjugacy in the dynamics of time of arrival operators
• Impact of a tunneling particle on the quantum state of a barrier: two-particle wave-packet model
• Canonical pairs in finite-dimensional Hilbert space