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Short distance modification of the quantum virial theorem
In this letter, we will analyse the deformation of a semi-classical
gravitational system from minimal measurable length scale. In the
semi-classical approximation, the gravitational field will be analysed as a
classical field, and the matter fields will be treated quantum mechanically.
Thus, using this approximation, this system will be represented by a
deformation of Schr\"odinger-Newton equation by the generalised uncertainty
principle (GUP). We will analyse the effects of this GUP deformed
Schr\"odinger-Newton equation on the behaviour of such a semi-classical
gravitational system. As the quantum mechanical virial theorem can be obtained
using the Schr\"odinger-Newton equation, a short distance modification of the
Schr\"odinger-Newton equation will also result in a short distance modification
of the quantum mechanical virial theorem.Comment: 16 page
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