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2019

Uncertainty principle in quantum mechanics with Newton's gravity

Kuzmichev, V. E., Kuzmichev, V. V.

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A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity.

The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is considered.
The potential energy is defined as a sum of `standard' non-gravitational term and the second one, which corresponds to gravitational attraction of particles as in Newton's theory of gravity.
The Green's function method is applied to solve the Schroedinger equation.

Uncertainty principle in quantum mechanics with Newton's gravity · Around

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C. Bambi, F.R. Urban. Natural extension of the generalised uncertainty principle. Class. Quant. Grav
Original
1965
Earlier work this paper cites.
A. Messiah, Quantum Mechanics
1967
Earlier work this paper cites.
S. Flügge, Practical Quantum Mechanics
Original
1971
Earlier work this paper cites.
L. de Broglie, Les incertitudes d’Heisenberg et l’interprétation probabiliste de la mécanique ondulatoire
1982
Earlier work this paper cites.
G. Veneziano. A stringy nature needs just two constants. Europhys. Lett
1986
Earlier work this paper cites.
D. Amati, M. Ciafaloni, G. Veneziano. Can spacetime be probed below the string size? Phys. Lett
1989
Earlier work this paper cites.
K. Konishi, G. Paffuti, P. Provero. Minimum physical length and the generalized uncertainty principle in string theory. Phys. Lett
1990
Earlier work this paper cites.
M. Maggiore. A generalized uncertainty principle in quantum gravity. Phys. Lett
1993
Earlier work this paper cites.

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