Motion of a wave packet in the Klein paradox

Nitta, H.; Kudo, Tomoshige; Minowa, H.

doi:10.1119/1.19174

Cited by 44 publications

(36 citation statements)

References 3 publications

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“…As a result of this Pauli blocking, the reflected electron gets entangled with the pair-creation process such that it cannot be described by a single-particle wave function. The suppression due to Pauli blocking is in contradiction to statements that the incoming electron can "knock-out" a positron under the barrier [4] or that the incoming electron "stimulates" [7] the pair-creation process.…”

contrasting

confidence: 63%

“…This classically forbidden nonvanishing transmission has been dubbed the "Klein paradox." Two types of approaches have been used to investigate this paradox [2][3][4][5][6][7][8][9][10][11][12]. The first group analyzed the dynamics in purely quantum-mechanical terms, which cannot predict any of the pair creation that is unavoidably associated with the supercritical barrier by itself.…”

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confidence: 99%

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Bosonic analog of the Klein paradox

Wagner

Ware

et al. 2010

Phys. Rev. A

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The standard Klein paradox describes how an incoming electron scatters off a supercritical electrostatic barrier that is so strong that it can generate electron-positron pairs. This fermionic system has been widely discussed in textbooks to illustrate some of the discrepancies between quantum mechanical and quantum field theoretical descriptions for the pair creation process. We compare the fermionic dynamics with that of the corresponding bosonic system. We point out that the direct counterpart of the Pauli exclusion principle (the central mechanism to resolve the fermionic Klein paradox) is stimulated emission, which leads to the resolution of the analogous bosonic paradox.In 1927 the Swedish scientist Oskar Klein [1] analyzed the quantum-mechanical solution of the Dirac equation for an incoming electron that scatters off a one-dimensional electrostatic barrier of height V . He observed a nonvanishing transmission if this height exceeds twice the rest mass energy of the electron (V > 2 mc 2 ), even for incoming energies E that are far below the potential height, E < V . This classically forbidden nonvanishing transmission has been dubbed the "Klein paradox." Two types of approaches have been used to investigate this paradox [2][3][4][5][6][7][8][9][10][11][12]. The first group analyzed the dynamics in purely quantum-mechanical terms, which cannot predict any of the pair creation that is unavoidably associated with the supercritical barrier by itself. The second approach used quantum field theory, which correctly describes the pair-creation process, but the effect of the incoming electron on the pair-creation process was not included. A complete description has to be quantum field theoretical and must include the incoming particle as well as the pair-creation process at the barrier.Numerical solutions to quantum field theory were used to study the interaction of the pair-creation process at the barrier with an incoming electron with full space-time resolution [10,11]. In agreement with earlier predictions, it was shown that the incoming electron suppresses the pair-creation process during the time it is being (completely) reflected at the barrier. The incoming electron occupies states that are therefore no longer available for the pair-creation process. As a result of this Pauli blocking, the reflected electron gets entangled with the pair-creation process such that it cannot be described by a single-particle wave function. The suppression due to Pauli blocking is in contradiction to statements that the incoming electron can "knock-out" a positron under the barrier [4] or that the incoming electron "stimulates" [7] the pair-creation process.While a wide number of articles have examined the Klein paradox in its historical fermionic context, an analogous analysis within the context of a bosonic system with spacetime resolution has found less attention [5,13]. There are several reasons for this. First, the threshold with regard to the electric field strength to break down the fermionic vacuum is easier to reach tha...

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confidence: 63%

mentioning

confidence: 99%

Bosonic analog of the Klein paradox

Wagner

Ware

et al. 2010

Phys. Rev. A

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“…Previous studies of the Klein paradox have been limited to theory [20][21][22][23], e.g. with phenomena analogous to the Klein paradox, possibly observable in graphene [24,25] or with single trapped ions [26].…”

Section: Klein Paradox Analoguementioning

confidence: 99%

Experimental investigation of strong field trident production

et al. 2010

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We show by experiment that an electron impinging on an electric field that is of critical magnitude in its rest frame, may produce an electron-positron pair. Our measurements address higher-order QED, using the strong electric fields obtainable along particular crystallographic directions in single crystals. For the amorphous material our data are in good agreement with theory, whereas a discrepancy with theory on the magnitude of the trident enhancement is found in the precisely aligned case where the strong electric field acts.

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“…Returning to our conundrum, we observe that in any formal numerical calculation, which ignores the antiparticle re-interpretation, the Klein paradox appears mathematically as the particular solution to a problem in which at t = −∞ we have two opposite moving wave packets: the incident wave packet at z = −∞ and the below potential wave packet (of appropriate size) at z = +∞. When these two meet at time t ∼ 0 at the step discontinuity z = 0 the continuity equations tell us that they unite and form a single wave packet, the reflected wave packet [20]. In this way probability is indeed seen to be conserved.…”

Section: Discussionmentioning

confidence: 99%