Phase-space representations via quasiprobability distributions
DOI:
https://doi.org/10.31349/RevMexFisE.23.020209Keywords:
Phase-Space Representation, Quasiprobability Distributions, Coherent States, Thermal Mean EnergyAbstract
Energy is a cornerstone concept in physics, embodying both conservation principles and the dynamics of systems. In quantum mechanics, energy manifests as the expectation value of the Hamiltonian operator, yet its intuitive understanding often remains elusive to students. This paper adopts a pedagogical approach to demystify quantum energy by employing three key phase-space representations: the Glauber-Sudarshan P-function, the Husimi Q-function, and the Wigner function. We show that, despite their distinct mathematical frameworks and interpretations, all three representations yield equivalent expressions for the mean energy of thermal states. This result provides an engaging platform for introducing concepts such as coherent states, operator ordering, and quasiprobability distributions. By bridging classical and quantum perspectives in an accessible format, we present a teaching model that not only conveys technical skills but also cultivates deeper conceptual insights, making it feasible to implement in a single lecture. This approach facilitates a richer understanding of the interplay between quantum mechanics and statistical physics, preparing students for advanced topics in quantum theory.
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