# Course Details for A.Y. 2018/2019

#### Name:

**Modern Physics / Modern Physics**

### Basic information

##### Credits:

*:* Master Degree in Mathematics 6 CFU (c)

##### Degree(s):

Master Degree in Mathematics 2^{nd} anno curriculum Generale Compulsory

##### Language:

Italian

### Course Objectives

The goal of this course is to introduce the students to basic concepts of modern physics, namely to special relativity and to the quantum nature of light and energy, emphasizing whenever possible, how classical concepts have shown up to be inadequate in explaining experiments. The experiments which will be analyzed are: a) optical aberration experiments, Michelson-Morley ether wind experiment, Black body radiation experiments in both Planck and Einstein views, temperature dependent specific heats, the photoelectric effect, Rutherford scattering, Compton scattering, optical emission and absorption spectra of atoms, X-ray emission spectra, diffraction of electrons.
On successful completion of this module, the student should have not only gained a deep understanding on the motivations that have led in the past century to the relativistic and quantum revolution in physics, but should also have become familiar with relativistic kinematics and mechanics and with the basic formulae describing the quantum nature of light and matter.

### Course Content

- Special relativity: Experiments on the nature and the speed of light. Failure of the ether theory.
Galileo an Lorentz transforms for coordinates and velocities. Minkowski space and space-time 4- vectors. Relativistic Doppler effect. Linear momentum, forces, energy and energy-momentum relation. Transform for electromagnetic fields and radiation. Energy-momentum 4-vector, rest mass and mass defective reactions.
- The quantum hypothesis: Black body radiation and Planck’s interpretation. Cathode rays, the photoelectric effect and Einstein’s light quanta. Boltzmann’s distribution, the specific heat problem and the quantum hypothesis. Light quanta and the black body spectrum. Compton scattering versus Thomson scattering. Einstein coefficients .
- Electronic structure of the atom: Failure of the Plum pudding model and the planetary model. Rutherford scattering and the size of the nucleus. Drawbacks of the planetary model and Balmer’s formula for the spectral lines of Hydrogen. Stationary states and Born’s atomic model. Correspondence principle and the Rydberg constant: reduced mass effect. Many electron atoms: X-ray emission spectra.
- Matter waves: De Broglie wavelength and the pilot wave. Stationary states and stationary waves. The Davisson-Germer experiment. Single and double slit experiments using waves, classical particles and quantum particles. Particles, wave packets and the basic requirements of the new theory: probability waves and the uncertainty principle.

### Assessment Methods and Criteria

Written and oral examination: three written test will be performed during the course, they can replace the written part of the final examination

### Textbooks

- A. Tipler, Fisica Moderna
* *
- Halliday, Resnick, Walker, Fisica Moderna
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- Mazzoldi, Nigro, Voci,, Fondamenti di Fisica
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- J. J. Brehm, W. J. Mullin, Introduction to the structure of matter: a course in modern physics
* *

### Notes

- Lecture notes in italian are available at the e-learning site http://www.didattica.univaq.it/moodle/ .

### Course page updates

This course page is available (with possible updates) also for the following academic years:

** To read the *** current * information on this course, if it is still available, go to the university course catalogue .
*Course information last updated on: 05 maggio 2016, 17:54*