Canonical hydrogenic orbitals are members of the family of solutions to the one-electron atom system. The properties of hydrogenic orbitals are well studied and presented in introductory courses in physics and chemistry. In this communication, we explore some lesser known properties of the hydrogenic orbitals: their behaviour in response to the momentum operator. It is observed that the local momentum associated with the hydrogenic orbital is locally complex-valued. It is also verified in this manuscript that the momentum of the hydrogenic orbital integrates to zero, satisfying the standing wave condition.
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Balakrishnan Viswanathan (2026) studied this question.
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