Physics Letters A 316 (2003) 168–172 www.elsevier.com/locate/pla Quantum particles inside Gaussian bags in (1 + 1) general relativity Gheorghe Ardelean ∗ , Ion I. Cot˘ aescu West University of Timi¸ soara, V. Pârvan Ave. 4, RO-1900 Timi¸ soara, Romania Received 24 March 2003; received in revised form 23 July 2003; accepted 23 July 2003 Communicated by P.R. Holland Abstract The quantum modes of massive scalar particles inside open bags generated by Gaussian conformaly flat (1 + 1) metrics are investigated. Using computational methods, it is shown that the energy spectrum is mixed having a finite discrete part and a continuous one. A specific behavior of the discrete levels to the limit of separation between these parts is pointed out.  2003 Elsevier B.V. All rights reserved. PACS: 04.62.+v; 03.65.Ge In general relativity there is the opportunity to see the quark confinement as a geometric effect produced by a bag inside which the free particles have periodic motions. The simplest models are of closed bags repre- sented as anti-de Sitter cavities [1,2] whose metrics re- produces the usual classical equations of motion of the nonrelativistic (isotropic) harmonic oscillator (HO) or the equidistant discrete energy spectrum of the quan- tum one [3]. Other models producing harmonic oscil- lations as well as more complicated periodic motions have been recently constructed using conformal trans- formations [4] or even deformations [5] of some de Sitter and anti-de Sitter metrics. It is remarkable that * Corresponding author. CGL, Fraunhofer Institute IISB, Schot- tkystr 10, 91058 Erlangen, Germany. E-mail addresses: ardelean@ww.uni-erlangen.de (G. Ardelean), cota@physics.uvt.ro (I.I. Cot˘ aescu). all these models have the same nonrelativistic limit, namely the nonrelativistic HO [4,5]. In general, the models with deformed anti-de Sitter metrics are of closed bags but those with deformed de Sitter metrics simulate open bags from which the particle can escape when its energy is enough. Since these models have hyperbolic metrics, recently we have proposed, as an alternative, a new classical model of open bag produced by a Gaussian (1 + 1) metric which is asymptotically flat [6]. We have shown that in this model the motion of the classical particle inside the bag is very close to a pure harmonic oscillation. This indicates that the corresponding quantum model could be successfully studied in the energy basis of the usual quantum HO. The present Letter is devoted to this problem. We consider the quantum model of a scalar test particle of the mass M freely moving inside the Gaussian bag simulated by the geometry of a (1 + 1)- 0375-9601/$ – see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016/S0375-9601(03)01155-1