Rectangular potentials

Iftika Philo Wardani, Nufida Dwi Aisyah, Adri Supardi

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.

Zafar Ahmed, Tanayveer Singh Bhatia, Shashin Pavaskar +1 more

We revisit a rectangular barrier as well as a rectangular well (pit) between two rigid walls. The former is the well known double-well potential and the latter is a hole potential. Let $|V_0|$ be the height (depth) of the barrier (well) then for a fixed geometry of the potential, we show that in the double-well, $E=V_0(>0)$, and in the hole potential ($V_0 <0$), $E=0$, can be energy eigenvalues provided $V_0$ admits some special discrete values. These states have been missed out earlier which emerge only when one seeks the special zero-energy solution of one-dimensional Schr{ö}dinger equation as $ψ(x)=Bx+C$.

Tapan Kumar Das

Hong Zhu

It is demonstrated that throughout the penetration of the rectangular potential barrier the probability current density J → remains constant