Problem Solving in Quantum Mechanics: From Basics to Real-World Applications for Materials Scientists, Applied Physicists, and Devices Engineers PDF
Preview Problem Solving in Quantum Mechanics: From Basics to Real-World Applications for Materials Scientists, Applied Physicists, and Devices Engineers
(cid:2) Problem Solving in Quantum Mechanics (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) Problem Solving in Quantum Mechanics From Basics to Real-World Applications for Materials Scientists, Applied Physicists, and Devices Engineers Marc Cahay Spintronics and Vacuum Nanoelectronics Laboratory, University of Cincinnati, USA (cid:2) (cid:2) Supriyo Bandyopadhyay School of Engineering, Virginia Commonwealth University, USA (cid:2) (cid:2) Thiseditionfirstpublished2017 ©2017JohnWiley&SonsLtd Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem, ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingor otherwise,exceptaspermittedbylaw.Adviceonhowtoobtainpermisiontoreusematerialfrom thistitleisavailableathttp://www.wiley.com/go/permissions. TherightofMarcCahayandSupriyoBandyopadhyaytobeidentifiedastheauthor(s)ofthis workhasbeenassertedinaccordancewithlaw. 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Cahay would like to thank the students who took his course on Quantum Systems taught at the University of Cincinnati over the last four years and who carefully checked many of the problems in this book, including (in alphabetic order): Joshua Alexander, Kelsey Baum, Graham Beach, Jordan Bishop, Ryan Blanford, Mike Bosken, Joseph Buschur, James Charles, Sumeet Chaudhary, Triet Dao, Aaron Diebold, Chelsey Duran, Adam Fornalczyk, Sthitodhi Ghosh, Adam Hauke, Erik Henderson, Phillip Horn, Alexander Jones, Henry Jentz, Jesse Kreuzmann, Alex Lambert, Craig Mackson, Ashley Mattson, James McNay, Thinh Nguyen, Francois Nyamsi, Jesse Owens, Nandhakishore Perulalan, Kaleb Posey, Logan Reid, Charles Skipper, Adam Steller, Matthew Strzok, William Teleger, Nicole Wallenhorst, Brian Waring, Aaron Welton, Samuel Wenke, and Robert Wolf. M. Cahay would like to thank his wife, Janie, for her support and patience during this time-consuming project. Supriyo Bandyopadhyay dedicates this book to his family and students. (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) Contents About the Authors ix Preface xi 1 General Properties of the Schr¨odinger Equation 1 2 Operators 15 3 Bound States 47 4 Heisenberg Principle 80 (cid:2) 5 Current and Energy Flux Densities 101 (cid:2) 6 Density of States 128 7 Transfer Matrix 166 8 Scattering Matrix 205 9 Perturbation Theory 228 10 Variational Approach 245 11 Electron in a Magnetic Field 261 12 Electron in an Electromagnetic Field and Optical Properties of Nanostructures 281 13 Time-Dependent Schr¨odinger Equation 292 A Postulates of Quantum Mechanics 314 B Useful Relations for the One-Dimensional Harmonic Oscillator 317 C Properties of Operators 319 vii (cid:2) (cid:2) viii Contents D The Pauli Matrices and their Properties 322 E Threshold Voltage in a High Electron Mobility Transistor Device 325 F Peierls’s Transformation 329 G Matlab Code 332 Index 343 (cid:2) (cid:2) (cid:2)
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