#### Presentation Title

Numerical Methods for Determining Eigenenergies and Tunneling Rates in One-Dimensional Quantum Wells

#### Faculty Mentor

Dr. Gerardo Dominguez

#### Start Date

18-11-2017 2:15 PM

#### End Date

18-11-2017 3:15 PM

#### Location

BSC-Ursa Minor 43

#### Session

Poster 3

#### Type of Presentation

Poster

#### Subject Area

physical_mathematical_sciences

#### Abstract

Astronomers have long been interested in the astrochemical processes that occur in the beginning stages of star formation in cold regions of the universe. It is well established that at the low temperatures of those regions, Hydrogen atoms are the ones that are most involved in diffusive mechanisms. However, recent studies have found that diffusion of heavier particles such as oxygen can also be effective suggesting that besides Hydrogen, Oxygen atoms are also mobile at very low temperatures. Here we present a theoretical investigation of the efficient diffusion of stable oxygen-isotopes via quantum tunneling through a one-dimensional subsequent potential. Oxygen-16, Oxygen-17, and Oxygen-18, which were considered as point particles, were originally confined in a one-dimensional finite potential quantum well and were expected to tunnel through a finite potential barrier. This presumption was tested using MATLAB, by which graphical and numerical solutions were computed in order to obtain eigenenergies for each isotope; afterwards the tunneling ratios and tunneling probability plots as well as the three-isotope plot of the oxygen isotopic composition were analyzed. Results show that diffusion of stable oxygen-isotopes via quantum tunneling is effective for different sized quantum wells. Surprisingly, stable oxygen isotopes that diffused through a finite quantum well having a set potential height of 0.07eV and a width of 0.7Å and that tunneled through a subsequent finite barrier with a set potential height of Vo and a barrier width ranging from 0.1Å to 3Å revealed mass-independent isotopic effects also referred as mass-independent fractionation, which was first discovered experimentally in 1983 by Mark H. Thiemens and Heidenreich.

Numerical Methods for Determining Eigenenergies and Tunneling Rates in One-Dimensional Quantum Wells

BSC-Ursa Minor 43

Astronomers have long been interested in the astrochemical processes that occur in the beginning stages of star formation in cold regions of the universe. It is well established that at the low temperatures of those regions, Hydrogen atoms are the ones that are most involved in diffusive mechanisms. However, recent studies have found that diffusion of heavier particles such as oxygen can also be effective suggesting that besides Hydrogen, Oxygen atoms are also mobile at very low temperatures. Here we present a theoretical investigation of the efficient diffusion of stable oxygen-isotopes via quantum tunneling through a one-dimensional subsequent potential. Oxygen-16, Oxygen-17, and Oxygen-18, which were considered as point particles, were originally confined in a one-dimensional finite potential quantum well and were expected to tunnel through a finite potential barrier. This presumption was tested using MATLAB, by which graphical and numerical solutions were computed in order to obtain eigenenergies for each isotope; afterwards the tunneling ratios and tunneling probability plots as well as the three-isotope plot of the oxygen isotopic composition were analyzed. Results show that diffusion of stable oxygen-isotopes via quantum tunneling is effective for different sized quantum wells. Surprisingly, stable oxygen isotopes that diffused through a finite quantum well having a set potential height of 0.07eV and a width of 0.7Å and that tunneled through a subsequent finite barrier with a set potential height of Vo and a barrier width ranging from 0.1Å to 3Å revealed mass-independent isotopic effects also referred as mass-independent fractionation, which was first discovered experimentally in 1983 by Mark H. Thiemens and Heidenreich.