On the Concept of Phase in Quantum Mechanics

V.V. Babikov

Ravo Tokiniaina Ranaivoson, Voriraza Séraphin Hejesoa, Raoelina Andriambololona +5 more

Wave-particle duality is often considered as the modern answer to the problem of the nature of light after more than 2000 years of questioning. It is also the answer given by quantum physics concerning the nature of matter particles and any other radiations. The main objective of this work is to analyze the relations that are existing between this concept of wave-particle duality, the uncertainty principle and the concepts of phase space and microstates considered in statistical mechanics. It is mainly highlighted that while the concepts of phase space and microstates were already introduced in classical physics before the discovery of the wave-particle duality, a correct understanding of them cannot be achieved without the use of the concept of quantum phase space and phase space representation of quantum mechanics which are directly related to the uncertainty principle. The possibility of using these concepts of quantum phase space and phase space representations of quantum mechanics to help in a deeper description of the wave-particle duality and in the study of some current issues related to foundational problems of quantum mechanics like quantum decoherence and the measurement problem is also discussed.

Aishwarya Parthasarathi, Dayanand Parashar, R. S. Kaushal

With a view to increasing the scope of applications of supersymmetric quantum mechanics (SUSY QM), we formulate the same in a complex phase space. Within this framework, the concept of shape invariance is reinvestigated and an insight into the eigenvalue spectra of non-Hermitian Hamiltonians is sought. The results are applied to a variety of potentials. We claim that the shape invariance for these potentials in the complex phase space can be retrieved in terms of the prescriptions already proposed in the conventional SUSY QM, in that the transformation of potential parameters takes the form of a reflection in the parameter space. Interestingly, some of these features turn out to be the generalization of the concept of quasi-parity used recently in the context of SUSY QM of PT-symmetric potentials. Further, a correspondence of the present approach with other complex formulations of SUSY QM and also in two real dimensions is demonstrated.

V.V. Babikov

V.V. Babikov

R. Loudon

The phase of a simple-harmonic vibration or wave is a useful and easily-understood concept in classical mechanics. It is the angle that determines the sinusoidal development of the motion, and it varies linearly with time, increasing by 360°(or 2π radians) over a complete cycle of oscillation. By contrast, the concept of phase in the quantum mechanics of harmonic motion has been fraught with difficulties, which have hampered its use. Recently, D T pegg and S M Barnett (Europhys. Lett. 6 483) have proposed a new definition of the quantum-mechanical phase operator, which they suggest will lead to important and far-reaching consequences.