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In quantum mechanics textbooks the momentum operator is defined in theCartesian coordinates and rarely the form of the momentum operator in sphericalpolar coordinates is discussed. Consequently one always generalizes theCartesian prescription to other coordinates and falls in a trap. In this workwe introduce the difficulties one faces when the question of the momentumoperator in spherical polar coordinate comes. We have tried to point out mostof the elementary quantum mechanical results, related to the momentum operator,which has coordinate dependence. We explicitly calculate the momentumexpectation values in various bound states and show that the expectation valuereally turns out to be zero, a consequence of the fact that the momentumexpectation value is real. We comment briefly on the status of the angularvariables in quantum mechanics and the problems related in interpreting them asdynamical variables. At the end, we calculate the Heisenberg's equation ofmotion for the radial component of the momentum for the Hydrogen atom.

Reality of linear and angular momentum expectation values in bound states