A comparison of the quantizations and supraquantization of the time of arrival for anharmonic oscillator potential

Abstract

Time of arrival (TOA) operators for anharmonic oscillator potential are obtained using Weyl, simple-symmetric, Born-Jordan quantization and supraquantization. The quantized TOA operators are compared to determine which is closest to the supraquantized TOA operator. The Wigner transform of the simple symmetric and Born-Jordan quantized diverge while the Weyl-quantized and the supraquantized vanish as the initial point, q, approaches the arrival point, implying that Weyl out of the three is the quantization that gives a TOA operator closest to the supraquantized TOA operator.