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Using Magnetic Resonance to Connect Newtonian Mechanics and Quantum Behavior

Using Magnetic Resonance to Connect Newtonian Mechanics and Quantum Behavior. Keith P. Madden, PhD. Ivy Tech Community College South Bend, IN. The Nature of the Problem. Nanotechnology revolution is here! Transition from macroscopic to microscopic systems.

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Using Magnetic Resonance to Connect Newtonian Mechanics and Quantum Behavior

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  1. Using Magnetic Resonance to Connect Newtonian Mechanics and Quantum Behavior Keith P. Madden, PhD.Ivy Tech Community CollegeSouth Bend, IN

  2. The Nature of the Problem Nanotechnology revolution is here! • Transition from macroscopic to microscopic systems. • New materials and processes operating at molecular size scale. • The behavior of these systems is not well explained using classical concepts.

  3. Colloidal quantum dots CdSe

  4. Spectrum of CdSeNanoparticles

  5. What Do Students Learn Now? Mostly mechanical /thermal systems, with the traditional development. My PHYS 101 topic list: 1 Introduction, Technical Measurements, Vectors, Translational Equilibrium, Friction (Measurements) 2 Torques & Rotational Equilibrium (Equilibrium) 3 Uniformly Accelerated Motion & Projectile Motion (Gravitational Acceleration) 4 Newton’s Second Law (Newton’s Second Law)

  6. What Do Students Learn Now? 5 Work, Energy and Power 6 Impulse and Momentum 7 Uniform Circ. Motion (Centripetal Acceleration) 8 Rotation of Rigid Bodies (Density of Materials) 9 Elasticity (Hooke’s Law & Hysteresis) 10 Fluids (Fluid Flow) 11 Temperature & Expansion Quantity of Heat 12 Heat Transfer (Specific Heat) 13 Thermal Properties, Thermodynamics, & Nanotechnology

  7. When and How Are Quantum Concepts Usually Introduced? • When math is considered sufficient Calculus, Systems of Linear Equations • After Physics 101 – 102, Classical Mechanics, and Electricity and Magnetism • A long time to wait in a two-year program! • We need to show the inadequacies of classical concepts – and the way past that problem.

  8. The Traditional Introduction:Paradoxical Nature of Light Dr. Thomas Young (1802) – light is a wave

  9. The Traditional Introduction:Paradoxical Nature of Light R.A. Millikan (1916) – light is a particle The electrons were emitted immediately - no time lag! 2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy! 3. Red light will not cause the ejection of electrons, no matter what the intensity! 4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths!

  10. The Traditional Introduction • The particle in a box • Advantages: Mathematically simple • Disadvantage: Correct solution to problem is not completely plausible.

  11. The Particle in a Box

  12. WavefunctionAmplitude WavefunctionAmplitude Squared

  13. What Does it Mean? • We have discrete energies for each state of the particle. • We have discrete positions for the particle. • If the barriers are not infinite, we have a finite probability of finding the particle outside the box. • What kind of bowling alley is this??

  14. Let’s Try a More Intuitive System

  15. Energy of a Bar Magnet in a Static Magnetic Field

  16. Magnetic Field of a Proton

  17. Precession of the Proton

  18. Free Precession of a Spin

  19. Similarity between Spinning Top and the Spinning Proton

  20. A Familiar Analogous Classical System

  21. In the Quantum Regime • The operators that are used to elucidate the proton system are: • S2 Total angular momentum squared • Sz Parallel angular momentum component • Sy Perpendicular a.m. component • SxPerpendicular a.m. component

  22. Precession with H0 and H1

  23. The Experiment • Build an NMR Pound box (only three transistors, and three diodes!) • Mix a sample of water (with a little copper sulfate to make it blue). • Insert sample in ~3300 Gauss magnetic field (permanent magnet or small electromagnet) • Observe absorption of R.F. energy ~13 MHz.

  24. The Experiment (con’t) • Vary magnetic field, observe proportional change in RF frequency. • Students can see quantum behavior in the most familiar substance – water. • Students can then experiment with gyroscope • to see quite analogous behavior between the classical and quantum versions of angular momentum.

  25. Conclusion • Quantum concepts can be made accessible early in the physics curriculum, but a quantum system with strong parallels to classical behavior is needed. • The gyroscope and the proton of water (H2O) fulfill this criterion. • A lab can be provided with simple (home-built) equipment to show the proton’s quantum transition (magnetic resonance).

  26. References • Pauling, L.; Wilson, E.B. Jr. Introduction to Quantum Mechanics, McGraw-Hill (1935). • http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html (and linked pages). • Wertz, J.E.,Bolton, J.R., Electron Spin Resonance, McGraw-Hill (1972).

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