1. Gravitational Radiation of Atom
The potentional energy of hydrogen-like atom equal to
where r is a distance from electron to nucleus, Ze is a nuclear charge, e is an electron charge, G is a gravitational constant, m is an electron mass, M is a nuclear mass.
equality (1) will have the form
To solve a Schrodinger equation for radial wave functions
we receive energy levels
To take into consideration that
we have finally
The two last members of equality (2) define the gravitational radiation of atom.
2. Planck's interval in Quantum Theory of Gravity
The rest mass of electron maybe equal
where h is Planck's constant, c is velocity of light, G is gravitational constant, k is numerical coefficient,
then Planck's four-dimensional interval
defines its limit of the localization in space-time.
If we utilize equality
Hamiltonian for free electron will have form
or we have
If we linearize the equation (1), we receive
For electron with charge e, which is in electromagnetic field, we do the substitution in equality (2)
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