Tunneling in energy eigenstates and complex quantum trajectories
Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show t...
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| Autor*in: |
Mathew, Kiran [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Chapman University 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Quantum studies - Berlin : Springer, 2014, 2(2015), 4 vom: 17. Juli, Seite 403-416 |
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| Übergeordnetes Werk: |
volume:2 ; year:2015 ; number:4 ; day:17 ; month:07 ; pages:403-416 |
| Links: |
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| DOI / URN: |
10.1007/s40509-015-0051-9 |
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| Katalog-ID: |
SPR036558044 |
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| 520 | |a Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. | ||
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| 700 | 1 | |a John, Moncy V. |4 aut | |
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10.1007/s40509-015-0051-9 doi (DE-627)SPR036558044 (SPR)s40509-015-0051-9-e DE-627 ger DE-627 rakwb eng Mathew, Kiran verfasserin aut Tunneling in energy eigenstates and complex quantum trajectories 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Chapman University 2015 Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. Complex quantum trajectory (dpeaa)DE-He213 Tunneling (dpeaa)DE-He213 Potential barrier (dpeaa)DE-He213 Soft potential step (dpeaa)DE-He213 John, Moncy V. aut Enthalten in Quantum studies Berlin : Springer, 2014 2(2015), 4 vom: 17. Juli, Seite 403-416 (DE-627)797383492 (DE-600)2785734-7 2196-5617 nnns volume:2 year:2015 number:4 day:17 month:07 pages:403-416 https://dx.doi.org/10.1007/s40509-015-0051-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 2 2015 4 17 07 403-416 |
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10.1007/s40509-015-0051-9 doi (DE-627)SPR036558044 (SPR)s40509-015-0051-9-e DE-627 ger DE-627 rakwb eng Mathew, Kiran verfasserin aut Tunneling in energy eigenstates and complex quantum trajectories 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Chapman University 2015 Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. Complex quantum trajectory (dpeaa)DE-He213 Tunneling (dpeaa)DE-He213 Potential barrier (dpeaa)DE-He213 Soft potential step (dpeaa)DE-He213 John, Moncy V. aut Enthalten in Quantum studies Berlin : Springer, 2014 2(2015), 4 vom: 17. Juli, Seite 403-416 (DE-627)797383492 (DE-600)2785734-7 2196-5617 nnns volume:2 year:2015 number:4 day:17 month:07 pages:403-416 https://dx.doi.org/10.1007/s40509-015-0051-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 2 2015 4 17 07 403-416 |
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10.1007/s40509-015-0051-9 doi (DE-627)SPR036558044 (SPR)s40509-015-0051-9-e DE-627 ger DE-627 rakwb eng Mathew, Kiran verfasserin aut Tunneling in energy eigenstates and complex quantum trajectories 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Chapman University 2015 Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. Complex quantum trajectory (dpeaa)DE-He213 Tunneling (dpeaa)DE-He213 Potential barrier (dpeaa)DE-He213 Soft potential step (dpeaa)DE-He213 John, Moncy V. aut Enthalten in Quantum studies Berlin : Springer, 2014 2(2015), 4 vom: 17. Juli, Seite 403-416 (DE-627)797383492 (DE-600)2785734-7 2196-5617 nnns volume:2 year:2015 number:4 day:17 month:07 pages:403-416 https://dx.doi.org/10.1007/s40509-015-0051-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 2 2015 4 17 07 403-416 |
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10.1007/s40509-015-0051-9 doi (DE-627)SPR036558044 (SPR)s40509-015-0051-9-e DE-627 ger DE-627 rakwb eng Mathew, Kiran verfasserin aut Tunneling in energy eigenstates and complex quantum trajectories 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Chapman University 2015 Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. Complex quantum trajectory (dpeaa)DE-He213 Tunneling (dpeaa)DE-He213 Potential barrier (dpeaa)DE-He213 Soft potential step (dpeaa)DE-He213 John, Moncy V. aut Enthalten in Quantum studies Berlin : Springer, 2014 2(2015), 4 vom: 17. Juli, Seite 403-416 (DE-627)797383492 (DE-600)2785734-7 2196-5617 nnns volume:2 year:2015 number:4 day:17 month:07 pages:403-416 https://dx.doi.org/10.1007/s40509-015-0051-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 2 2015 4 17 07 403-416 |
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10.1007/s40509-015-0051-9 doi (DE-627)SPR036558044 (SPR)s40509-015-0051-9-e DE-627 ger DE-627 rakwb eng Mathew, Kiran verfasserin aut Tunneling in energy eigenstates and complex quantum trajectories 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Chapman University 2015 Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. Complex quantum trajectory (dpeaa)DE-He213 Tunneling (dpeaa)DE-He213 Potential barrier (dpeaa)DE-He213 Soft potential step (dpeaa)DE-He213 John, Moncy V. aut Enthalten in Quantum studies Berlin : Springer, 2014 2(2015), 4 vom: 17. Juli, Seite 403-416 (DE-627)797383492 (DE-600)2785734-7 2196-5617 nnns volume:2 year:2015 number:4 day:17 month:07 pages:403-416 https://dx.doi.org/10.1007/s40509-015-0051-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 2 2015 4 17 07 403-416 |
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Mathew, Kiran |
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Mathew, Kiran misc Complex quantum trajectory misc Tunneling misc Potential barrier misc Soft potential step Tunneling in energy eigenstates and complex quantum trajectories |
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Tunneling in energy eigenstates and complex quantum trajectories Complex quantum trajectory (dpeaa)DE-He213 Tunneling (dpeaa)DE-He213 Potential barrier (dpeaa)DE-He213 Soft potential step (dpeaa)DE-He213 |
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Tunneling in energy eigenstates and complex quantum trajectories |
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tunneling in energy eigenstates and complex quantum trajectories |
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Tunneling in energy eigenstates and complex quantum trajectories |
| abstract |
Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. © Chapman University 2015 |
| abstractGer |
Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. © Chapman University 2015 |
| abstract_unstemmed |
Abstract Complex quantum trajectory approach, which arose from a modified de Broglie–Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft potential step, plotted in a previous work, show that more trajectories link the left and right regions of the barrier, when the energy is increased. In this paper, we evaluate the reflection probability using a new ansatz based on these observations, as the ratio between the total probabilities of reflected and incident trajectories. While doing this, we also put to test the complex-extended probability density previously postulated for these quantum trajectories. The new ansatz is preferred since the evaluation is solely done with the help of the complex-extended probability density along the imaginary direction and the trajectory pattern itself. The calculations are performed for a rectangular potential barrier, symmetric Eckart and Morse barriers, and a soft potential step. The predictions are in perfect agreement with the standard results for potentials such as the rectangular potential barrier. For the other potentials, there is very good agreement with standard results, but it is exact only for low and high energies. For moderate energies, there are slight deviations. These deviations result from the periodicity of the trajectory pattern along the imaginary axis and have a maximum value only as much as %$0.1\,\%%$ of the standard value. Measurement of such deviation shall provide an opportunity to falsify the ansatz. © Chapman University 2015 |
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Tunneling in energy eigenstates and complex quantum trajectories |
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https://dx.doi.org/10.1007/s40509-015-0051-9 |
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John, Moncy V. |
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