Geometric description of the Schrödinger equation in $(3n+1)$-dimensional configuration space - INSPIRE

DataBETA

Geometric description of the Schrödinger equation in $(3n+1)$ -dimensional configuration space

M. Abdul Wasay
(
- U. Agric., Faisalabad and
- Quaid-i-Azam U.
)
,
Asma Bashir
(
- U. Agric., Faisalabad
)
,
Benjamin Koch
(
- Pontificia U. Catol. Chile, Santiago and
- Chile U., Catolica
)
,
Abdul Ghaffar
(
- U. Agric., Faisalabad
)

Mar 29, 2017

12 pages

Published in:

Int.J.Geom.Meth.Mod.Phys. 14 (2017) 10, 1750149

Published: Aug 18, 2017

e-Print:

1703.09901 [hep-th]

DOI:

10.1142/S0219887817501493

View in:

reference search5 citations

Citations per year

Abstract: (arXiv)

We show that for non-relativistic free particles, the (bosonic) many particle equations can be rewritten in geometric fashion in terms of a classical theory of conformally stretched spacetime. We further generalize the results for the particles subject to a potential.

Note:

6 pages

04.20.Cv
03.65.Ta
Geometric dual
Schrödinger equation
configuration space
Schroedinger equation
nonrelativistic
space-time

References(32)

Figures(0)

[1]

STATISTICAL INTERPRETATION OF THE KLEIN-GORDON EQUATION IN TERMS OF THE SPACE-TIME WEYL CURVATURE

E. Santamato
(
- Naples U.
)

- J.Math.Phys. 25 (1984) 2477-2480,
- J. Math. Phys. 25 ( 1984) 2477-2480
•
DOI:
- 10.1063/1.526467

[1]

GAUGE INVARIANT STATISTICAL MECHANICS AND AVERAGE ACTION PRINCIPLE FOR THE KLEIN-GORDON PARTICLE IN GEOMETRIC QUANTUM MECHANICS

E. Santamato
(
- Naples U.
)

- Phys.Rev.D 32 (1985) 2615-2621,
- Phys. Rev. D32 ( 1985) 2615-2621
•
DOI:
- 10.1103/PhysRevD.32.2615

[4]

Gravity and the quantum potential

Robert Carroll
(
- Illinois U., Urbana
)

e-Print:
- gr-qc/0406004

[3]

Nonminimal scalar-tensor theories and quantum gravity

F. Shojai
(
- Iran U. Sci. Tech. and
- IPM, Tehran and
- Tarbiat Modarres U.
)
,
A. Shojai
(
- Iran U. Sci. Tech. and
- IPM, Tehran and
- Tarbiat Modarres U.
)

- Int.J.Mod.Phys.A 15 (2000) 1859-1868
•
e-Print:
- gr-qc/0010012
•
DOI:
- 10.1016/S0217-751X(00)00080-X

[3]

Quantum, gravity and geometry

A. Shojai
(
- Tarbiat Modarres U. and
- IPM, Tehran
)

- Int.J.Mod.Phys.A 15 (2000) 1757-1771
•
e-Print:
- gr-qc/0010013
•
DOI:
- 10.1016/S0217-751X(00)00077-X

[3]

Quantum Einstein's equations and constraints algebra

Fatimah Shojai
(
- Iran U. Sci. Tech. and
- IPM, Tehran
)
,
Ali Shojai
(
- Tarbiat Modarres U. and
- IPM, Tehran
)

- Pramana 58 (2002) 13-19
•
e-Print:
- gr-qc/0109052
•
DOI:
- 10.1007/s12043-002-0002-y

[3]

Understanding quantum theory in terms of geometry

Fatimah Shojai
(
- IPM, Tehran
)
,
Ali Shojai
(
- IPM, Tehran and
- Tehran U.
)

•
e-Print:
- gr-qc/0404102

[4]

Gravity and the quantum potential

Robert Carroll
(
- Illinois U., Urbana
)

e-Print:
- gr-qc/0406004

[5]

Some remarks on Ricci flow and the quantum potential

Robert Carroll
(
- Illinois U., Urbana
)

e-Print:
- math-ph/0703065

[6]

The Ricci flow on Riemann surfaces

- JP J.Geom.Topol. 9 (2009) 215-223
•
e-Print:
- 0810.2236

[6]

A Mechanics for the Ricci flow

- Int.J.Geom.Meth.Mod.Phys. 6 (2009) 759-767
•
e-Print:
- 0810.2356
•
DOI:
- 10.1142/S0219887809003825

[7]

Relativistic Bohmian mechanics from scalar gravity

Benjamin Koch
(
- Chile U., Catolica
)

e-Print:
- 0810.2786

[8]

Quantizing Geometry or Geometrizing the Quantum?

Benjamin Koch
(
- Chile U., Catolica
)

- AIP Conf.Proc. 1232 (2010) 1, 313-320
•
e-Print:
- 1004.2879
•
DOI:
- 10.1063/1.3431507

[9]

Geometrizing the Quantum - A Toy Model

Benjamin Koch
(
- Chile U., Catolica
)

- AIP Conf.Proc. 1196 (2009) 1, 161
•
e-Print:
- 1004.3240
•
DOI:
- 10.1063/1.3284379

[10]

Entropic force, noncommutative gravity and un-gravity

Piero Nicolini
(
- Frankfurt U., FIAS
)

- Phys.Rev.D 82 (2010) 044030
•
e-Print:
- 1005.2996
•
DOI:
- 10.1103/PhysRevD.82.044030

[11]

Remarks on gravity and quantum mechanics

Robert Carroll
(
- Illinois U., Urbana
)

e-Print:
- 1007.4744

[12]

On the noncommutative eikonal

- Int.J.Geom.Meth.Mod.Phys. 8 (2011) 621-638
•
e-Print:
- 1007.4929
•
DOI:
- 10.1142/S0219887811005294

[13]

An Angular Formalism for Spin One Half

Benjamin Koch
(
- Chile U., Catolica
)
,
Nicolas Rojas
(
- Chile U., Catolica
)

- Int.J.Geom.Meth.Mod.Phys. 11 (2014) 1450029
•
e-Print:
- 1101.4619
•
DOI:
- 10.1142/S0219887814500297

[14]

An entropic picture of emergent quantum mechanics

D. Acosta
(
- Pinar del Rio U.
)
,
P. Fernandez de Cordoba
(
- Valencia, Polytechnic U.
)
,
J.M. Isidro
(
- Valencia, Polytechnic U.
)
,
J.L.G. Santander
(
- Valencia U.
)

- Int.J.Geom.Meth.Mod.Phys. 9 (2012) 1250048
•
e-Print:
- 1107.1898
•
DOI:
- 10.1142/S021988781250048X

[15]

Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas

S.Hamid Mehdipour
(
- Islamic Azad U., Lahijan
)

- Eur.Phys.J.Plus 127 (2012) 80
•
e-Print:
- 1111.2468
•
DOI:
- 10.1140/epjp/i2012-12080-4

[16]

Splitting the source term for the Einstein equation to classical and quantum parts

T.S. Biró
(
- Budapest, RMKI
)
,
P. Ván
(
- Budapest, RMKI
)

- Found.Phys. 45 (2015) 11, 1465-1482
•
e-Print:
- 1312.1316
•
DOI:
- 10.1007/s10701-015-9920-7

[17]

Bohmian particle trajectories in relativistic bosonic quantum field theory

Hrvoje Nikolic
(
- Boskovic Inst., Zagreb
)

- Found.Phys.Lett. 17 (2004) 363-380
•
e-Print:
- quant-ph/0208185
•
DOI:
- 10.1023/B:FOPL.0000035670.31755.0a

[18]

A New pilot-wave model for quantum field theory

- AIP Conf.Proc. 844 (2006) 1, 321-339
•
e-Print:
- quant-ph/0602229
•
DOI:
- 10.1063/1.2219372

[19]

Higher-dimensional geometric description of the quantum Klein-Gordon equation

Benjamin Koch
(
- Chile U., Catolica
)

- Int.J.Geom.Meth.Mod.Phys. 10 (2013) 9, 1320014
•
DOI:
- 10.1142/S0219887813200144

[20]

The Amplituhedron

- JHEP 10 (2014) 030
•
e-Print:
- 1312.2007
•
DOI:
- 10.1007/JHEP10(2014)030

1-25 of 32
1
2
25 / page