# Keith P. Madden, PhD. Ivy Tech Community College South Bend, IN

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Keith P. Madden, PhD. Ivy Tech Community College South Bend, IN
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. New materials and processes operating at molecular size scale. The behavior of these systems is not well explained using classical concepts.

Colloidal quantum dots
CdSe

Spectrum of CdSe Nanoparticles

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)

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

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.

Dr. Thomas Young (1802) – light is a wave

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!

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

The Particle in a Box

Wavefunction Amplitude
Squared

What Does it Mean? What kind of bowling alley is this??
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??

Let’s Try a More Intuitive System

Energy of a Bar Magnet in a Static Magnetic Field

Magnetic Field of a Proton

Precession of the Proton

Free Precession of a Spin

Similarity between Spinning Top and the Spinning Proton

A Familiar Analogous Classical System

S2 Total angular momentum squared
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 Sx Perpendicular a.m. component

Precession with H0 and H1

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.

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.

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).

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