Reality of linear and angular momentum expectation values in bound states

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dc.creatorRoy, Utpal
dc.creatorGhosh, Suranjana
dc.creatorShreecharan, T.
dc.creatorBhattacharya, Kaushik
dc.date2007-04-03
dc.date.accessioned2026-07-07T07:55:18Z
dc.date.available2026-07-07T07:55:18Z
dc.descriptionIn quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian prescription to other coordinates and falls in a trap. In this work we introduce the difficulties one faces when the question of the momentum operator in spherical polar coordinate comes. We have tried to point out most of the elementary quantum mechanical results, related to the momentum operator, which has coordinate dependence. We explicitly calculate the momentum expectation values in various bound states and show that the expectation value really turns out to be zero, a consequence of the fact that the momentum expectation value is real. We comment briefly on the status of the angular variables in quantum mechanics and the problems related in interpreting them as dynamical variables. At the end, we calculate the Heisenberg's equation of motion for the radial component of the momentum for the Hydrogen atom.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0704.0373
dc.identifierhttp://arxiv.org/abs/0704.0373
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126919
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.titleReality of linear and angular momentum expectation values in bound states
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