Quantum time of arrival for the cubic potential using the Weyl basis operators

Abstract

The quantum time of arrival for the cubic potential was obtained using the time-energy canonical commutation relation [H,T] = iħ1, where H is the Hamiltonian and T is the time of arrival operator. The Weyl basis operators T_m,n arising from the Weyl quantization, were used to find a meaningful time operator conjugate with the system Hamiltonian. This process can be extended in different basis, where the results can be compared to verify the uniqueness of time operators in potentials of order greater than 2.