Mario Belloni Davidson College

P.O. Box 561, 306 Pine Road Department of Physics

Research

August 1999-present: Starting at Davidson College, I have established a theoretical research program involving undergraduates. This research program is in the area of theoretical and computational quantum mechanics as these topics are readily accessible to undergraduates. I have successfully engaged eight students in my quantum-mechanics research program. I have received a Research Corporation grant to support this research, originally focusing on supersymmetric quantum mechanics (SUSY QM). In addition, I have engaged students in one-, two-, and three-dimensional quantum-mechanics research focusing on the time development of wave packets. We have three state-of-the-art computer workstations to support this research. In addition to working with undergraduates at Davidson, I have been working with Richard Robinett and Michael Doncheski of Pennsylvania State University studying fundamental quantum-mechanical systems.

Students

Leah Ruckle (physics ‘12)

Seyi Ayorinde (physics ‘10)

Kelsey Chisholm (physics ‘10)

David Sheibley (physics ‘07)

Robert Correll (physics ‘07)

Laura Gilbert (physics ‘06): now at Dartmouth College pursuing a Ph. D. in physics.

Kevin Bell (Spanish ’05)

Adam Abele (physics ‘03)

Andrew Schoewe (physics ‘03)

Ben Sargent (mathematics ‘01): now at University of Rochester pursuing a Ph. D. in astrophysics.

Tim Valdez (physics ‘01)

Student Awards/Honors

Summer 2011: Davidson College DRI Fellowship to Leah Ruckle (’12).

September 2006: Best Undergraduate Student Paper Award from the North Carolina Section of the American Association of Physics Teachers.  Award given to David Sheibley (’07).

May 2006: 76-page Honors Thesis, “An Analytic Study of the Quantum-mechanical Asymmetric Infinite Square Well,” completed by Laura Gilbert (’06).

April 2006:  Physics Award at Davidson College.  Award given to Laura Gilbert (’06).

March 2006:  Best Undergraduate Student Paper Award from the North Carolina Section of the American Association of Physics Teachers.  Award given to Laura Gilbert (’06).

October 2005:  Outstanding Undergraduate Student Award from the North Carolina Section of the American Association of Physics Teachers.  Award given to Laura Gilbert (’06).

April 2005: Sigma Xi Undergraduate Research Award.  Award given to Laura Gilbert (’06) for research completed with Mario Belloni.

April 2003: Sigma Xi Undergraduate Research Award.  Award given to Adam Abele (’03) for research completed with Wolfgang Christian and Mario Belloni.

Professional Service/Outreach/Leadership

July 2010-July 2011: Interim Society of Physics Students Zone Councilor from Zone 5,.

September 2005: Attend the 2005 SPS and Sigma Pi Sigma National Council Meeting as proxy Zone Councilor from Zone 5, Washington, D.C.

September 2005: Attend the 2005 SPS and Sigma Pi Sigma National Council Meeting as proxy Zone Councilor from Zone 5, Washington, D.C.

Publications with Undergraduates (denoted by a *)

June 2010: “New Mathematical Identities from Quantum Mechanical Sum Rules: Parity-related Potentials,” Seyi Ayorinde*, Kelsey Chisholm*, Mario Belloni, and Richard W. Robinett, J. Phys. A: Mathematical and Theoretical, 43 235202, 22 pp. (2010).

November 2006: “Piecewise Zero-curvature Energy Eigenfunctions in One Dimension,” Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, European Journal of Physics 27, 1331-1339 (2006).

June 2006: “Playing Quantum Physics Jeopardy with zero-energy eigenstates,” Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, American Journal of Physics 74, 1035-1036 (2006). ArXiv number: quant-ph/0606196.

September 2005: “More on the Asymmetric Infinite Square Well: Energy Eigenstates with Zero-curvature,” Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, European Journal of Physics 26, 815-825 (2005). ArXiv number: quant-ph/0512156.

Web Publications

June 2006: “Playing Quantum Physics Jeopardy with zero-energy eigenstates,” Laura Gilbert, Mario Belloni, Michael Doncheski, and Richard Robinett.  Content to support the paper of the same name published in The American Journal of Physics.  Available at:  http://webphysics.davidson.edu/mjb/jeopardy.  This material is also published as EPAPS Document E-AJPIAS-72-xxxxxx at: ftp://ftp.aip.org/epaps/am_j_phys/E-AJPIAS-72-xxxxxx/.

Talks and Presentations given at Davidson College with Undergraduates (*)

September 2010: Leah Ruckle*, Mario Belloni, and Richard Robinett “The Biharmonic Oscillator and Asymmetric Linear Potentials in the Extreme Quantum Limit,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

September 2009: Seyi Ayorinde*, Kelsey Chisholm*, Wolfgang Christian, Richard Robinett, and Mario Belloni, “Negativity of the Wigner Function and its Applications,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

September 2009: Kelsey Chisholm*, Seyi Ayorinde*, Richard Robinett, and Mario Belloni, “New Mathematical Identities from Quantum Mechanical Sum Rules: Parity-related Potentials,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

August 2006: David Sheibley* and Mario Belloni, “Studying a Quantum ‘Bounce’,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

August 2006: Robert Correll*, Mario Belloni, and Wolfgang Christian, “Packets in the Classical Asymmetric Infinite Square Well,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

April 2006: Laura Gilbert*, “An Analytic Study of Quantum Mechanical Asymmetric Infinite Square Wells,” Honors Thesis Defense, Physics Department, Davidson College.

April 2006: Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, “An Analytic Study of Quantum Mechanical Asymmetric Infinite Square Wells,” Invited Poster, Decision Davidson.

September 2005: Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, “Wigging out for the Summer: How I Learned to Stop Worrying and Love Phase Space in Quantum Mechanics,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

September 2004: Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, “Much Ado About Nothing: A Diversion into Allowable Solutions of the 1-D Schrödinger Equation,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

Summer 2004: Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, “Wave Packet Revivals in the Asymmetric Infinite Square Well,” Contributed Talk, Davidson College Physics Department’s Summer Research Symposium at Davidson College.

May 2003: Adam Abele*, “Using Java 3D to Visualize Calculations in Advanced Quantum Mechanics,” Poster, Spring Research Symposium at Davidson College.

May 2003: Adam Abele*, “Using Java 3D to Visualize Calculations in Advanced Quantum Mechanics,” Contributed Talk, Physics Department Seminar at Davidson College.

September 2002: Kevin Bell* and Andrew Schoewe*, “Through the Looking Glass:  An Introduction to Supersymmetry, SUSY Quantum Mechanics, and Complex Periodic Potentials,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

Summer 2002: Kevin Bell* and Andrew Schoewe*, “Through the Looking Glass:  An Introduction to Supersymmetry, SUSY Quantum Mechanics, and Complex Periodic Potentials,” Contributed Talk, Davidson College Physics Department’s Summer Research Symposium at Davidson College.

August 2001: Ben Sargent*, “PT-Symmetric Supersymmetric Quantum Mechanics,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

Summer 2001: Ben Sargent*, “PT-Symmetric Supersymmetric Quantum Mechanics,” Contributed Talk, Davidson College Physics Department’s Summer Research Symposium at Davidson College.

October 2000: Tim Valdes*, “Supersymmetric Quantum Mechanics,” Math Coffee, Mathematics Department at Davidson College.

September 2000: Tim Valdes*, “Supersymmetric Quantum Mechanics,” Contributed Talk, Davidson College Physics Department’s “What I Did on My Summer Vacation” Seminar at Davidson College.

Summer 2000: Tim Valdes*, “Supersymmetric Quantum Mechanics,” Contributed Talk, Davidson College Physics Department’s Summer Research Symposium at Davidson College.

May 2000: Tim Valdes*, “Supersymmetric Quantum Mechanics,” Poster, Spring Research Symposium at Davidson College.

1998: Matthew Fagen*, “SUSY,” Talk given as part of a Junior/Senior seminar course at Eckerd College.

1998: Brian Evans*, “Neutrino Mixing,” Talk given as part of a Junior/Senior seminar course at Eckerd College.

Conference Talks and Presentations with Undergraduates (*)

October 2010: Leah Ruckle*, Mario Belloni, and Richard Robinett “The Biharmonic Oscillator and Asymmetric Linear Potentials in the Extreme Quantum Limit,” Joint Meeting of the North Carolina Section of the American Association of Physics Teachers and Zone 9 of the Society of Physics Students, Davidson, North Carolina.

October 2010: Todd Timberlake, Aaron Titus, Mark Montazer*, and Mario Belloni, “A Flexible Platform for Teaching Astronomy and Astrophysics,” Contributed Poster, North Carolina Astronomers’ Meeting, Raleigh, North Carolina.

February 2010: T. Timberlake, A. Titus, M. Montazer*, and M. Belloni, “A Flexible Platform for Teaching Astronomy and Astrophysics,” Contributed Poster, Joint Winter Meeting of the American Association of Physics Teachers and American Physical Society, Washington, DC.

January 2007: D. Sheibley*, M. Belloni, M. A. Doncheski, and R. W. Robinett, “Studying a Quantum ‘Bounce’,” Contributed Talk, Joint Winter Meeting of the American Association of Physics Teachers and the American Astronomical Society, Seattle, WA, January 2007.

January 2007: R. Correll*, M. Belloni, and W. Christian, “Packets in the Classical Asymmetric Infinite Square Well,” Contributed Talk, Joint Winter Meeting of the American Association of Physics Teachers and the American Astronomical Society, Seattle, WA, January 2007.

September 2006: David Sheibley* and Mario Belloni, “Studying a Quantum ‘Bounce’,” Contributed Poster, Joint Meeting of the North Carolina Section of the American Association of Physics Teachers and Zone 9 of the Society of Physics Students, Elon, North Carolina.

September 2006: Robert Correll*, Mario Belloni, and Wolfgang Christian, “Packets in the Classical Asymmetric Infinite Square Well,” Contributed Poster, Joint Meeting of the North Carolina Section of the American Association of Physics Teachers and Zone 9 of the Society of Physics Students, Elon, North Carolina.

April 2006: M. A. Doncheski, R. W. Robinett, L. P. Gilbert*, and M. Belloni, “Fun with a Square Well,” Contributed Talk, Central Pennsylvania Section of the American Association of Physics Teachers, Pennsylvania College of Technology, Williamsport, Pennsylvania.

March 2006: Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, “An Analytic Study of  Quantum Mechanical Asymmetric Infinite Square Wells,” Contributed Poster, Joint Meeting of North Carolina Section of the American Association of Physics Teachers and Zone 9 of the Society of Physics Students, Belmont, North Carolina.

November 2005: Mario Belloni, Laura Gilbert*, Michael Doncheski, and Richard Robinett, “An Analytic Study of Energy Eigenstates of Piecewise-constant Potentials Using the Wigner Quasi-probability Distribution,” Contributed Talk, Joint Meeting of the Southeastern Section of the American Physical Society and the Florida Section of the American Association of Physics Teachers, Gainesville, Florida.

October 2005: Laura Gilbert*, “The Pedagogy of the Asymmetric Infinite Square Well,” Invited Talk, North Carolina Section of the American Association of Physics Teachers, Pembroke, North Carolina.

January 2005: Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, “Wave Packet Revivals in the Asymmetric Infinite Square Well,” Contributed Talk, Winter Meeting of the American Association of Physics Teachers, Albuquerque, New Mexico.

October 2004: Mario Belloni, Laura Gilbert*, Michael Doncheski, and Richard Robinett, “Much Ado About Nothing: A Diversion into Allowable Solutions of the 1-D Schrödinger Equation,” Contributed Talk, Joint Meeting of North Carolina Section of the American Association of Physics Teachers and Zone 9 of the Society of Physics Students, Davidson, North Carolina.

October 2004: Laura Gilbert*, Mario Belloni, Michael Doncheski, and Richard Robinett, “Wave Packet Revivals in the Asymmetric Infinite Square Well,” Contributed Poster, Joint Meeting of North Carolina Section of the American Association of Physics Teachers and Zone 9 of the Society of Physics Students, Davidson, North Carolina.

November 2003: Kevin Bell*, Andrew Schoewe*, and Mario Belloni, “Hill’s Equation and SUSY QM: Solving Periodic PT-symmetric Differential Equations,” Contributed Poster, Joint Meeting of the Southeastern Section of the American Physical Society and the North Carolina Section of the American Association of Physics Teachers, Wilmington, North Carolina.

August 2003: Mario Belloni, Adam Abele*, and Wolfgang Christian, “One-, Two-, and Three-dimensional Quantum Mechanics Using Java3D,” Contributed Talk, Summer Meeting of the American Association of Physics Teachers, Madison, Wisconsin.

April 2003: Adam Abele*, “Using Java 3D to Visualize Problems in Classical and Quantum Mechanics,” Invited Poster, Sigma Xi Undergraduate Research Awards, Charlotte, North Carolina.

April 2003: Kevin Bell*, Andrew Schoewe*, and Mario Belloni, “Using Hill’s Equation to Solve PT-Symmetric Periodic Differential Equations,” Contributed Talk, Joint Meeting of the American Physical Society and the Division of Particles and Fields, Philadelphia, Pennsylvania.

January 2003: Andrew Schoewe*, Kevin Bell* and Mario Belloni, “Solving PT-Symmetric Periodic Potentials Using Hill’s Equation,” Contributed Talk, Winter Meeting of the American Association of Physics Teachers, Austin, Texas.

June 2002: Mario Belloni, Kevin Bell*, Ben Sargent*, and Andrew Schoewe*, “Determining the Energy Spectrum of a PT-Symmetric Periodic Potential,” Contributed Poster, Gordon Research Conference on Physics Research and Education: Quantum Mechanics, South Hadley, Massachusetts.

March 2002: Mario Belloni and Meghan Carroll*, “Using a Computer-Rich Curriculum to Teach Quantum Mechanics,” Contributed Talk, North Carolina Section of the American Association of Physics Teachers, Winston Salem, North Carolina.

January 2002: Ben Sargent* and Mario Belloni, “PT-Symmetric Periodic Potentials within Supersymmetric Quantum Mechanics,” Contributed Talk, Winter Meeting of the American Association of Physics Teachers, Philadelphia, Pennsylvania.

November 2001: Ben Sargent* and Mario Belloni, “PT-Symmetric Supersymmetric Quantum Mechanics,” Contributed Poster, Southeastern Section of the American Physical Society, Charlottesville, Virginia.