Drew Kerr
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Drew Kerr's document discusses boundary conditions in quantum mechanics and their potential application to braneworld cosmology. It introduces braneworld theory and standard quantum mechanics concepts like the Schrodinger equation. It then examines non-standard boundary conditions for a particle in a box, which could allow a particle to be bound at the boundary. A lattice model is constructed whose continuum limit has unusual boundary conditions. The document suggests these non-standard boundary conditions may help explain braneworld theory and identifies writing a paper on boundary conditions in quantum mechanics as a future goal.
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The document discusses the growth of ZnSnN2, a group II-IV nitride semiconductor. It provides background on group II-IV nitrides and their potential applications. It then details experimental efforts to synthesize ZnSnN2 using a high vacuum plasma system, including considerations for suppressing zinc evaporation and removing zinc oxide layers. Initial growth attempts at 400°C and 500°C are reported, with the lower temperature growth potentially yielding ZnSnN2 but requiring further analysis. Overall progress is made but full optimization of growth conditions is still needed.
Kaytlin Brinker Presentation
Kaytlin Brinker modeled proton exchange membrane fuel cells by developing equations to describe the charge distribution in the Stern layer and diffuse layer of the membrane. Her results showed that including the charge imbalance in the membrane is important for calculating fuel cell properties accurately. For future work, she plans to use molecular modeling software to simulate proton diffusion in Nafion under varying hydration conditions and predict transport properties from a theoretical diffusion model.
Jermaine Taylor Presentation
Experimental detectors are being developed to search for signals from extraterrestrial intelligence at optical wavelengths using lasers, motivated by the possibility that civilizations may communicate over interstellar distances with nanosecond laser pulses. The proposed design involves an optical telescope with multiple Fresnel lenses in a 3x3 array, each focusing light onto an array of photomultiplier tubes to detect any rapid flashes that could indicate laser pulses from space. The goal is to create a low-cost system that can monitor regions of the sky continuously over long periods with minimal human involvement.
Jason Mast Presentation
This document summarizes two methods for fabricating suspended nanowire structures. Method 1 involves carving trenches in silicon dioxide and dropping nanowires over the trenches. Method 2 embeds nanowires between layers of photoresist and creates metallic contacts. The goals are to fabricate suspended nanowire devices and test their I-V curves. While alignment was too complicated in Method 1, Method 2 successfully produced suspended nanowire structures and preliminary I-V curve measurements.
Courtney Klosterman Presentation
This document summarizes a presentation on organic photovoltaic solar cells. It discusses how organic solar cells use a bulk heterojunction of p-type and n-type organic polymers to generate electricity from light absorption. Calculations show thinner polymer layers could optimize light absorption through a cavity effect. The presenter's goal is to verify experimentally that thinner polymer layers in different electrode configurations can absorb as much light as thicker layers. Preliminary results with commercial ITO, polymer and silver layers show agreement with calculations for a 66.1nm thick polymer layer. Further work will optimize materials and structures to improve efficiencies and enable mass production of organic solar cells.
James Arnemann Presentation
This document summarizes calculations done to determine the effective masses in the semiconductor ZnGeN2. It outlines using the Full Potential LMTO method to calculate energy bands as a function of the Brillouin zone. From this, parabolas were fit to determine effective masses close to zero k. These masses were then used in a modified Wurtzite Hamiltonian to calculate the energy vs. k relationship and understand properties of ZnGeN2.
Christine Austin Presentation
The document discusses magnetic resonance imaging (MRI) technology. It describes how MRI works by using a large superconducting magnet to align protons in the body with its magnetic field. Radio frequency pulses are then used to excite the protons, causing their magnetization to precess. Coils are designed on computers and etched onto circuit boards to transmit and receive the radio signals involved in the MRI process.
Sustainability 101
Our Sustainability Time Line provides key dates in Case Western Reserve University's sustainability efforts over the past two decades including starting a campus recycling program in 1996, launching an energy management effort in 1998, and completing the first greenhouse gas inventory in 2008. The document defines sustainability, triple bottom line, greening, renewable energy, carbon footprint, and greenhouse gases. It provides tips for greening the office, home, and commute.
More from Case Western Reserve University - College of Arts and Sciences (16)
Drew Kerr
- 1. Thinking Outside the Box About Branes in Cosmology Drew Kerr Austin Peay State University REU Mentors: Harsh Mathur, Kate Jones-Smith Case Western Reserve University Collaborator: AnirudhDasarathy Hawken School
- 3. Quantum Mechanics in the Continuum
- 5. Quantum Mechanics on a Lattice
- 7. Higher Dimensions
- 9. The Free Particle V = 0 The Free Particle Schrodinger Equation is satisfied by the solution: Energy State:
- 10. The Particle in a Box Boundary Condition Solution Quantized Energy States
- 11. The Particle in a Potential Step Incoming Plane Wave Reflecting Plane Wave
- 12. What Boundary Conditions are allowed in a box? Any boundary condition that satisfies Hermiticity may be imposed.
- 13. Non-standard Boundary Conditions Scattering Solution “Penetration Depth” parameter Bound Solution Particle lives here
- 15. The Lattice Model Scattering Solution Bound Solution
- 17. Boundary conditions that are permissible but non-standard may be relevant to Brane Physics in cosmology and to Topological Insulators in solid state physics
- 18. We construct a lattice model whose continuum limit has unusual boundary conditions.
Editor's Notes
- In classical mechanics a particle can be described exactly by its momentum and position. In quantum mechanics however, one can only describe a particle by its wave function, or probability of being in some state. This yields a statistical interpretation for quantum mechanics solutions.Note: the indicated momentum operator is more like the operator squaredThe Schrodinger equation can be satisfied by Psi being a plane wave
- *note the difference between the QUANTIZED energy of the particle in the box versus the energy of the free particle
- -scattering states
- We don’t have to worry about it-we found the extra dimensions curled up on campus!
- Here is the Schrodinger equation for our model of a one-sided lattice.By determining the reflection coefficient, we find a continuum prediction for the bound energy of the particle on the lattice.And by solving the bound state, we find the exact bound energy of the particle on the lattice.
- Not just Psi=0