Abstract

Despite the large literature on hydrogen-like atoms, one cannot find any mention as to how long an electron spends in the orbit to generate the quanized radiation energy En. Here, the Heisenberg representation of operators is exteded so as to be able to deal also with imverse oprators. This is necessary when dealing with Coulomb potentials. This then allows to write down the general hydrogen-like atom in a compact form. With the help of operator algebra that includes also the inverse operators, one arrives at the differential equation of the electron trajectory with respect to time.The time solution is achieved through established coupled integral equations. While already established quantized radiation electron energy En is proportional to 1/n2, the newely derived quantized electron circular time tn(e) is proportional to n3 with n=1,2,3,..,and tn(e) being of the order of 10−16 sec in magnitude.

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