Quantum Physics/Chapter 1

Quantum Physics, 2nd Ed.

Stephen Gasiorowicz

• 1. The Limits of Classical Physics
• 2. Wave Packets and the Uncertainty Relations
• 3. The Schrodinger Wave Equation and the Probability Interpretations
• 4. Eigenfunctions and Eigenvalues
• 5. One-dimensional Potentials
• 6. The General Structure of Wave Mechanics
• 7. Operator Methods in Quantum Mechanics
• 8. N-Particle Systems
• 9. The Schrodinger Equation in Three Dimensions I
• 10. The Schrodinger Equation in Three Dimensions II
• 11. Angular Momentum
• 12. The Hydrogen Atom
• 13. Interactions of Electrons with Electromagnetic Fields
• 14. Operators, Matrices, and Spin
• 15. The Addition of Angular Momentum
• 16. Time-Independent Perturbation Theory
• 17. The Real Hydrogen Atom
• 18. The Helium Atom
• 19. The Structure of Atoms
• 20. Molecules
• 21. The Radiation of Atoms
• 22. Selected Topics in Radiation Theory
• 23. Collision Theory
• 24. The Absorption of Radiation in Matter
• Appendix A. The Fourier Integral and the Delta Functions
• Appendix B. Operators
• Special Topic 1. Relativistic Kinematics
• Special Topic 2. The Density Operator
• Special Topic 3. The Wentzel-Kramers-Brillouin Approximation
• Special Topic 4. Lifetimes, Linewidths, and Resonances

Intro

This chapter covers some of the exciting problems physicists faced at the end of the 19th Century.

Overview

Discoveries of how black body radiation, the photoelectric effect, the Compton Effect, and the structure of the atom lead to the discovery that:

• Light behaves like a particle.
• The light particles have quantized energy.
• Matter such as electrons behave like waves

Blackbody Radiation

<math>E(\lambda, T)</math> is the emissive power at wavelength <math>\lambda</math> at temperature <math>T</math>.

<math>A(\lambda)</math> is the absorptivity at wavelength <math>\lambda</math>, the fraction of energy absorbed.

Kirchoff noted in 1859 that the ratio <math>E/A</math> is the same for all bodies over all temperatures and wavelengths.

For a black body (<math>A = 1</math>), E is a universal function.

If we imagine a black body as a box with a small hole, then we can see that the energy being emitted from the hole does not come from reflection of the surfaces inside. We can imagine energy moving from surface to surface, and calculate the energy density:

<math>u(\lambda, T) = {4 E(\lambda, T) \over c}</math>

Wilhelm Wien shows in 1894 that the energy density was:

<math>u(\lambda, T) = \lambda ^{-5}f(\lambda T)</math>

Switching the frequency in:

<math>u(\nu, T) = \nu^3 g(\nu / T)</math>

Now, we need only look at one temperature and a variety of frequencies and wavelengths, and we can find f or g.