Chapter 11. Basics of the modern theory of many-particle systems

Michael V. Sadovskii

Supathorn Phongikaroon

This chapter will explore Einstein’s theory of special relativity. In addition, readers will find the basic concept of radiation as waves and particles including photoelectric and Compton scattering effects. Definition of X-ray and behaviors under conservation of momentum and energy will be provided and discussed. Various photon and particle wavelengths will be explored with various examples to help readers understand how to apply basic quantum theory dealing with the de Broglie wavelength, wave equation, wave–particle duality, and the uncertainty principle.

Paul C. Martin, Julian Schwinger

Maciej Lewenstein, Anna Sanpera, V. Ahufinger

Abstract This chapter explains the basic ideas and concepts of the modern quantum theory of condensed matter. It starts by discussing phase transition in classical systems, scaling, and renormalisation theory, both in real and in momentum space. The chapter then moves on to quantum systems and discusses Bose–Einstein condensation (BEC) in non-interacting gases. It presents the concept of quantum phase transitions, illustrating it with spin systems and BEC in weakly interacting gases. Finally, the chapter discusses specific properties of low dimensional Bose systems: the role of phase fluctuations in 1D and 2D gases, Tonks-Girardeau gas in 1D, and Berezinskii-Kosterlitz-Thouless transition in 2D.

Nitin Ramchandra Gadre

The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.

Stephen J. Gustafson, Israel Michael Sigal