Abstract Quantum tunneling occurs in the isomerization of hydroxymethylene into formaldehyde. Experiments and theory have proven the occurrence of it but both of them have a different result of the half-life of 0.7 hours. The differences the result is the motivation in this study. In theoretical, the probability of quantum tunneling calculates by Wentzel, Kreamer, Berlioun (WKB) approximation. This study calculates probability quantum tunneling use WKB and rectangular function approximation. The calculation of quantum tunneling probability with rectangular function approximation started at 1, 3, 5, 7 until 59 rectangular functions potential barrier use transfer matrix method to simplify the calculation. We use Gaussian function as the potential barrier that the height and width of the potential barrier satisfy the character of the potential barrier in isomerization hydroxymethylene barrier to formaldehyde. And the result, we get the minimum number of rectangular potential barrier to obtain a stable quantum tunneling probability value of 35 potential.Abstract Quantum tunneling occurs in the isomerization of hydroxymethylene into formaldehyde. Experiments and theory have proven the occurrence of it but both of them have a different result of the half-life of 0.7 hours. The differences the result is the motivation in this study. In theoretical, the probability of quantum tunneling calculates by Wentzel, Kreamer, Berlioun (WKB) approximation. This study calculates probability quantum tunneling use WKB and rectangular function approximation. The calculation of quantum tunneling probability with rectangular function approximation started at 1, 3, 5, 7 until 59 rectangular functions potential barrier use transfer matrix method to simplify the calculation. We use Gaussian function as the potential barrier that the height and width of the potential barrier satisfy the character of the potential barrier in isomerization hydroxymethylene barrier to formaldehyde. And the result, we get the minimum number of rectangular potential barrier to obtain a stable quantum tunneling probability value of 35 potential.

Journal of Physics Conference SeriesJan 1, 20201 citation

TUNNELLING IN RECTANGULAR BARRIER SYSTEMS

WORLD SCIENTIFIC eBooksDec 1, 19860 citations

Classical tunneling

Arthur Cohn, Mario Rabinowitz

arXiv:physics/0306009International Journal of Theoretical PhysicsMar 1, 199015 citations

Time dependence of the probability density in the transient regime for tunneling

Gastón García‐Calderón, Jorge Villavicencio

An exact analytical solution to the time-dependent Schr\"odinger equation with cutoff wave initial conditions is used to investigate the fast tunneling response of a rectangular potential barrier. We find that just across the tunneling region, the probability density exhibits at short times a transient behavior that may be characterized by a peak ${t}_{p}$ and a width $\ensuremath{\Delta}t.$ We show that ${t}_{p}$ provides the earliest tunneling response of the system and that the top-barrier S-matrix poles play an important role in the process. As a function of the barrier width, ${t}_{p}$ exhibits two regimes. Along the first regime, ${t}_{p}$ remains almost a constant; as the barrier width increases, a second regime appears where ${t}_{p}$ grows linearly with the barrier width.An exact analytical solution to the time-dependent Schr\"odinger equation with cutoff wave initial conditions is used to investigate the fast tunneling response of a rectangular potential barrier. We find that just across the tunneling region, the probability density exhibits at short times a transient behavior that may be characterized by a peak ${t}_{p}$ and a width $\ensuremath{\Delta}t.$ We show that ${t}_{p}$ provides the earliest tunneling response of the system and that the top-barrier S-matrix poles play an important role in the process. As a function of the barrier width, ${t}_{p}$ exhibits two regimes. Along the first regime, ${t}_{p}$ remains almost a constant; as the barrier width increases, a second regime appears where ${t}_{p}$ grows linearly with the barrier width.

Physical Review AJun 15, 200147 citations

Quantal tunneling through a rectangular barrier using ‖ ψ ‖2 and flux

James E. Draper

The transmission coefficient for quantal tunneling through a rectangular, one-dimensional potential barrier is analyzed. By employing continuity of ‖ ψ ‖2 and flux the results, even with an asymmetrical barrier, are obtained easily. The asymmetrical barrier has the same transmission in either direction. Considerable insight into the form of the most physical quantity, ‖ ψ(x) ‖2, is afforded with little algebra. Graphs of transmission are given for general barriers, and properties of the solutions are discussed.The transmission coefficient for quantal tunneling through a rectangular, one-dimensional potential barrier is analyzed. By employing continuity of ‖ ψ ‖2 and flux the results, even with an asymmetrical barrier, are obtained easily. The asymmetrical barrier has the same transmission in either direction. Considerable insight into the form of the most physical quantity, ‖ ψ(x) ‖2, is afforded with little algebra. Graphs of transmission are given for general barriers, and properties of the solutions are discussed.

American Journal of PhysicsSep 1, 19803 citations

Tunneling on a macroscopic scale

Eugene M. Chudnovsky, Javier Tejada

Cambridge University Press eBooksAug 28, 19981 citation

{t}_{p}

and a width $\ensuremath{\Delta}t.$ We show that

{t}_{p}

provides the earliest tunneling response of the system and that the top-barrier S-matrix poles play an important role in the process. As a function of the barrier width,

{t}_{p}

exhibits two regimes. Along the first regime,

{t}_{p}

remains almost a constant; as the barrier width increases, a second regime appears where

{t}_{p}

grows linearly with the barrier width.