Exact vs. quasi-classical tunneling times for idealized potentials

Shegelski, Mark R. A.; Reid, M. M.; Holenstein, Roman

doi:10.1139/p01-072

Cited by 3 publications

(5 citation statements)

References 10 publications

(16 reference statements)

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“…This is in accord with our findings using idealized potentials [1]. That t WKB qc does not give a proper indication of the tunneling time merits repeating two comments.…”

Section: Resultssupporting

confidence: 89%

“…Our findings are the same as for piece-wise constant potentials [1] in that the quasi-classical time differs significantly when compared to a fully quantum mechanical tunneling time.…”

Section: Introductionsupporting

confidence: 81%

“…Recently, it was shown that the dwell time definition for tunneling times, as defined in the Copenhagen interpretation, agrees with the tunneling time in the Bohmian interpretation [9]. This is important because our definition of the tunneling time from initially localized states [1] is very similar to that defined in ref. 9.…”

Section: Expressions For the Tunneling Timesmentioning

confidence: 64%

“…In our first paper [1], an exact expression for ψ(x, t) was given. We solved the time-independent Schrödinger equation so that ψ(x, t) be expressed in terms of the energy eigenstates and energy eigenvalues.…”

Section: Expressions For the Tunneling Timesmentioning

confidence: 99%

“…In a previous paper [1], we compared an expression for a quantum mechanical tunneling time with the quasi-classical tunneling time for idealized potentials. We chose the potentials to be piece-wise constant (i.e., square wells and square potential barriers).…”

Section: Introductionmentioning

confidence: 99%

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Quantum mechanical versus quasi-classical tunneling times for smooth potential barriers

Shegelski

Kozijn²

2003

Can. J. Phys.

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For smooth potential barriers, we compare the quasi-classical tunneling time with an expression that gives a fully quantum mechanical tunneling time. The expression we choose for the quantum mechanical tunneling time is one that has heuristic value. We report results wherein this quantum mechanical tunneling time and the quasi-classical time differ significantly, both quantitatively and qualitatively. To determine the reasons for these differences, we compare the trends in the two times that result from varying the potential. Our findings suggest that, for smooth potential barriers, the quasi-classical tunneling time is unreliable for many cases where it is employed. PACS Nos.: 03.65Xp, 03.65-w Résumé : Nous comparons les temps d'effet tunnel pour des potentiels doux, tels que donnés par une théorie semi-classique et par un calcul purement quantique. Les résultats pour le temps d'effet tunnel quantique sont choisis pour leur valeur heuristique. Nous rapportons des résultats où les temps d'effet tunnel semi-classique et quantique diffèrent significativement, à la fois quantitativement et qualitativement. Afin de déterminer les raisons derrière ces différences, nous comparons la façon dont les deux temps évoluent sous une variation du potentiel. Nos résultats suggèrent que pour des potentiels doux, le temps d'effet tunnel semi-classique est incorrect dans beaucoup de cas où nous l'utilisons.[Traduit par la Rédaction]

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“…This is in accord with our findings using idealized potentials [1]. That t WKB qc does not give a proper indication of the tunneling time merits repeating two comments.…”

Section: Resultssupporting

confidence: 89%

“…Our findings are the same as for piece-wise constant potentials [1] in that the quasi-classical time differs significantly when compared to a fully quantum mechanical tunneling time.…”

Section: Introductionsupporting

confidence: 81%

Section: Expressions For the Tunneling Timesmentioning

confidence: 64%

Section: Expressions For the Tunneling Timesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum mechanical versus quasi-classical tunneling times for smooth potential barriers

Shegelski

Kozijn²

2003

Can. J. Phys.

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Tipping time of a quantum rod

Shegelski

Lundeberg

Goodvin

2005

American Journal of Physics

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We study the tipping time of a quantum mechanical rod that is constrained to move in a plane in a gravitational potential. The initial state of the center of mass of the rod is localized within the base of support of the rod. The tipping time is found to increase exponentially with the height H of the rod as C1t0 exp[C2(H/H0)9], where C1 and C2 are dimensionless constants of order one, t0 is the time scale of the motion, and H0 is the length scale of the rod. We show that the tipping time cannot be obtained using the uncertainty principle alone, and compare our result to that obtained using the Wentzel–Kramers–Brillouin approximation.

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Long tipping times of a quantum rod

Lundeberg¹,

Shegelski²

2006

Can. J. Phys.

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We calculate the tipping time of a quantum rod that has a height several times that of the edge length of its square base. We use an expression for the tipping time that has heuristic value, and gives the average time at which, upon measurement, the initially balanced rod is found to tip. We use two methods to calculate the tipping time. One method is to examine the "late time" behaviour of the quantum state of the center of mass of the rod by using an equation that has the form of the time-independent Schrödinger equation except that it involves a "complex energy." The other method uses energy resonances in the eigenstates of the Hamiltonian to determine the tipping time. We use the well-known WentzelKramersBrillouin approximation to calculate the energy eigenstates. With these methods, we obtain expressions for the tipping time that are valid for very long tipping times. PACS Nos.: 03.65.w, 03.65.Xp

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Exact vs. quasi-classical tunneling times for idealized potentials

Cited by 3 publications

References 10 publications

Quantum mechanical versus quasi-classical tunneling times for smooth potential barriers

Quantum mechanical versus quasi-classical tunneling times for smooth potential barriers

Tipping time of a quantum rod

Long tipping times of a quantum rod

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