# A time of arrival operator for a quartic oscillator potential from the Moyal bracket formalism

## Abstract

We construct a phase space time of arrival (TOA) function 𝒯(*q*,*p*) for the case of a quartic oscillator potential from its Moyal backet with the system Hamiltonian in quantum phase space, instead of the usual Poisson bracket in classical mechanics. We show that 𝒯(*q*,*p*) appears as an infinite series expanded in even powers of *ħ* with the classical arrival time 𝒯_{0}(*q*,*p*) appearing only as the leading term. We then show that the Weyl quantization of 𝒯(*q*,*p*) is exactly the supraquantized TOA operator for a quartic oscillator. This strongly suggests the possibility of using canonical quantization to construct TOA operators that generally satisfy the conjugacy requirement with the system Hamiltonian.

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*Proceedings of the Samahang Pisika ng Pilipinas*

**40**, SPP-2022-1D-04 (2022). URL: https://proceedings.spp-online.org/article/view/SPP-2022-1D-04.