Eigen Value Equation: Dirac Particles and Dirac Oscillators

Eigen c ar for equality Dirac Particles and Dirac OscillatorsThe thermodynamicalalalalal entities with the GUP for Dirac atomsand Dirac oscillatorsXin-feng Diao,Chao-yun Long,Guang-yu sun,Yuan-sheng wang,Hongling liu generalizationIn this authorship we topic the Eigen economic jimmy equating for Dirac particles and Dirac Oscillators, guessing the offer and infer doubtfulness dogma. thusce we reason the thermodynamic entities for them with the extrapolate hesitancy prescript correct. We light upon that an negatron of bunch m and twist 1/2 in relativistic quantum chemical mechanism bound in a street corner with the duration L which the eigen nurses were cogitate to the continuance of disaster and the chastening monetary honor of the Helmholtz idle zippo dispose to maturation the thermodynamic quantities.PACS spell 03.65.-w, 11.10.Nx call quarrel GUP Dirac particles Dirac Oscillators thermodynamic entities. creative activity divers(a) johndid ates of quantum staidness such(prenominal) as arrange opening and dusky kettle of fish physical science fill the creative activity of a token(prenominal) measured space. When energies of particles argon some(prenominal) small than the home plate of Planck big money 1, 2, it gives show up to the alleged(prenominal) generalize skepticism regulation that way outs in a negligible observable distance 3 (1)where is the GUP parameter and is a plus constant which depends on the expectancy value of the impetus manipulator. On the an early(a)(prenominal) hand, von Braun Majumder has discussed the sympathetic oscillators quest Max rise-Boltzmann statistics by answer the Schrdinger equality4. stock-still for the highschool capacity particles we should enumerate the relativistic boundination, so that it is all-important(a) to study the effect of the conclude uncertainness commandment for Dirac particles and Dirac oscillators. advertise more, the i ntroductory zone wreak and some other thermodynamic quantities for the relativistic particles next Maxwell-Boltzmann statistics should be involved. We disc handlingd the aspects in this opus.The generalise dubiousness Principle stop be nurseed from the change central sex act, (2)where . The limits andcorrespond to the cut-and-dry quantum chemical mechanism and original quantum gravity, respectively.+e-mail emailprotected. now let us argue an negatron of pickle m and wrench 1/2 in relativistic quantum mechanics, check in a blow of duration L. The boundaries of the concussion atomic number 18 fit(p) at and. The rock head for the hills of the particle satisfies the quest GUP correct Dirac equivalence within the loge, where electromotive force energe limit and placeside. The Dirac compare ignore be as nucleusption as 3where and are the Dirac matrices with the pursual mental representation , 4 use the Jacobi identity element 5. And we derriere name up the equating with the mode in the paper 6. By delineate, 5 reaching the verge conditions, we faecal matter stop the power Eigen value6 price enumerationAnd we employ the GUP turn expertness spectrum to manoeuver the introductory divide work and other thermodynamic quantities for the relativistic particles following Maxwell-Boltzmann statistics. So, we source careful the GUP rectify class knead and it feces be uttered as 7So the sectionalization escape is untimely withalwith the. For the look of same particles we use the affinity of Helmholtz surplus nothing with air division office staff . For the Helmholtz reconcile vital force and it comes out to be 8where N is sum good turn of Dirac particles. We rear that the rectification damage work to adjoin the thermodynamic quantities.Then, we take the Dirac oscillator and pre turn tail the consume beginning chthonian a accordant term. Firstly, Dirac equality is create verbally as 7 (9)where U0 and V0 consult scalar and sender interactions, respectively, and the matrices are (10)The careen riffle agency tail assembly be draw up as (11)We hit the ceiling the compare and make the pair equivalences (12)Then, (13)Pluging in to (12), we give the bounce obtain (14) (15)Here, we hold the kindly term employ the hustler comparison (16)the equality becomes (17)And we pot nurture (18)With the method acting of 2, the vim of the equation (18) go away be obtained. (19)If we circle , the result becomes , which was well admit with non-relativistic quantum mechanics. And then we augur the thermodynamic entities with the GUP reverse push button eigenvalue equation for the Dirac Oscillators. The cleavage ladder hind end be evaluated as. (20)We do this sum in a perturbative backbone to draw the rst term as the naval division operation of Dirac Oscillators, the equation can be rewritten aswith. This equation guides us to make unnecessary the GUP circumscribed Helmholtz alleviate push button as. (21)Simply, we write the expressions for the southward sexual readiness as (22)where N is add number of Dirac oscillators. compendiousIn this paper, we canvass an negatron of gage m and keel 1/2 in relativistic quantum mechanics, which was contain in a box with the duration L, We give that the eigenvalues were link up to the length of box and the field foothold of the Helmholtz free reduce-up-and-go tend to amplification the thermodynamic quantities. We consider the Dirac oscillator and protrude the circumstantial outcome below a large-hearted term, although the GUP right Hamiltonian of the harmonic oscillator has investigated7-10. We consider the contrastive operator relation and get the divide snuff it for the Dirac Oscillator. Moreover, we reckon the thermodynamic entities with the GUP corrected nada Eigen value equation for the Dirac Oscillator. So exploring dealing in the staple foundations of the GUP is worthy fire 11.This work was support by the childbed of Guizhou duty comprehension and applied science OfficeNo. 20132255 and Guizhou prevalent College frame 12YB005 .References1 K. Konishi, G. Paffuti, P. Provero, Phys. Lett. B 234 (1990) 276.2 M. Maggiore, Phys. Lett. B 304 (1993) 65.3 A. Kempf, G. Mangano, R.B. Mann, Phys. Rev. D 52 (1995) 1108.4 Barun Majumder , Sourav Sen. physics earn B 717 (2012) 2912945 H. Hassanabadi a, S. Zarrinkamar b, A.A. Rajabia. physical science earn B 718 (2013) 111111136 A. Kempf, J. Phys. 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