臺灣博碩士論文加值系統

The phase operator defined by quantization electromagnetic fi eld is still incompletely. This phase operator Phi is in doubt because annihilation and creation operators of a harmonic oscillator a and a^{dagger} respectively have the same index and e^{iPhi} is not Unitary by de finition of Dirac. Susskind and Glogower [2] operator E not only satisfi ed the index relation of a and a^{dagger} but also is a well-known defi nition even E is still not Unitary. In this thesis, we will point out the inconsistency in Susskind and Glogower defi nition and discuss the proper phase operator defi ned by Smith and Vaccaro.

Abstract . . . . . . . . . . . . . . . . . . . . . . . i
List of figures . . . . . . . . . . . . . . . . . . . . iv
Acknowledgments . . . . . . . . . . . . . . . . . . . . v
Introduction . . . . . . . . .. . . . . . . . . . . . . 1
1 Overview of Quantum Phase Operator . . . . . . . . . 7
1.1 Dirac's Phase Operator . . . . . . . . .. . . . . . 8
1.2 SG's Phase Operator . . . . . . . . . ... . . . . . 9
1.3 Pegg and Barnett's Phase Operator . . . . ..... . . 13
1.4 Phase Measurement . . . . . . . . . . . . . ... . . 15
1.4.1 Young's Double-splits Experiment . ............ . 15
1.4.2 Experimental Scheme . . . . . . . ........... . . 17
2 A Critical Analysis of SG Operator .. . . . . . . . . 22
2.1 More Discussions on The SG Operator . ....... . . . 22
2.2 Another Form of Eigenvalues of E . . . . .... . . . 24
2.3 The Domain of The Phase . . . . . . . . . ...... . 27
2.3.1 Classical Simple Harmonic Oscillator . ...........27
2.3.2 Quantum Phase . . . . . . . . . . . . . ..........28
3 Discussion A New Quantum Phase . . . . . . . . . . . 32
3.1 A New Quantum Phase . . . . . . . . . . . ....... . 32
3.1.1 Lewis, Lawrence and Harris's Denition ............32
3.1.2 Smith and Vaccaro's Comment . . . ............... 34
3.1.3 Davidovic Family and Arsenovic Com-ment . . . . . 35
3.2 Discussion on Eigenvalues of The Phase Operators... 37
3.2.1 SG's Operator . . . . . . . . . . . . . . ........37
3.2.2 SV's Phase Operator . . . . . . . . . . ..........38
3.2.3 Consistency Checking . . . . . . . . . ...........44
Conclusion . . . . . . . . . . . . . . . . . . . . . . 50
References . . . . . . . . . . . . . . . . . . . . . . 51

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