Short distance modification of the quantum virial theorem

Abstract

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 Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

arXiv comment16 pages

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Cited by in corpus (10)

• Challenges for $\Lambda$CDM: An update
• GUP Modified Hawking Radiation in Bumblebee Gravity
• Minimal Length Effects on Chaotic Motion of Particles around Black Hole Horizon
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
• A tale of analogies: gravitomagnetic effects, rotating sources, observers and all that
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• Two dimensional electron gas in a non-Euclidean space
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• Minimal Length Effects on Motion of a Particle in Rindler Space