Quantum Physics of Light and Matter - Relativistic Wave Equations

  • Luca Salasnich

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This video deals with the equation of relativistic quantum mechanics. It is divided in 6 segments.

The first segment introduces the quantization rules for relativistic systems and the Klein-Gordon equation.

The second segment derives and discusses the Dirac equation, while the third segment explains the non relativistic limit of the Dirac equation.

The fourth segment derives the Pauli equation from the Dirac equation in the presence of a magnetic field and the spin of the electron; the fifth considers the Dirac equation in a central potential and its conserved quantities, and the last segment studies the relativistic hydrogen atom by using the Dirac equation discussing its energy spectrum and the so-called fine structure corrections to the Bohr spectrum.

The ideal viewer is a MSc or PhD student of Physics or Chemistry or Engineering, who will learn how to quantize a relativistic system, the problems related to the Klein-Gordon and Dirac equations, the main properties of the spin of the electron, and the relativistic fine-structure corrections of the Bohr formula of the energy levels of the hydrogen atom.

Introduction

A short but rigorous explanation of relevant and characteristic quantum properties of light from an expert in the field.

About The Author

Luca Salasnich

Luca Salasnich is an Associate Professor of Theoretical Physics of Matter at University of Padova, Italy. He was previously a research scientist with the Italian National Research Council (CNR). Dr. Salasnich was awarded an MSc in Physics by the University of Padova in 1991, and his PhD in Theoretical Physics by the University of Florence in 1995. His fields of research are condensed matter theory and statistical physics, in particular nonlinear phenomena and macroscopic quantum effects (like superfluidity and superconductivity) in ultra-cold atomic gases and other many-body systems. At the University of Padova, Dr. Salasnich is a member of the Scientific Committee of Area 2 (Physical Sciences) and President of the Teaching Council for the BSc in Optics and Optometrics. He has written more than 130 scientific papers for international journals, with over 2500 citations.

 

About this video

Author(s)
Luca Salasnich
DOI
https://doi.org/10.1007/978-3-030-63296-0
Online ISBN
978-3-030-63296-0
Total duration
49 min
Publisher
Springer, Cham
Copyright information
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

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Video Transcript

[MUSIC PLAYING]

We are now ready to discuss another interesting video. This video is about the relativistic wave equations, mainly the relativistic equations of quantum mechanics.

This is the introduction. First, I will discuss the first attempt to derive a relativistic equation for quantum mechanics that is the so-called Klein-Gordon equation.

Then, we will move to the Dirac equation, that is the main object of the relativistic quantum mechanics, discussing the non relativistic limit of the Dirac equation that gives, as expected, the Schrodinger equation. But if we include also an external magnetic field, actually, you will see that we will not recover, strictly speaking, the Schrodinger equation, but an equation that is called the Pauli equation, which has a new object inside, mainly the spin of the particle.

Then, we will consider the Dirac equation in the case of a central potential. In particular, we will focus on the relativistic hydrogen atom showing that the quantization of the energy levels adopting the Dirac equation is similar but not equal to Bohr quantization and not relativistic for quantization. And the corrections to Bohr quantization due to the relativistic hydrogen atom based on the Dirac equation are the so-called fine splitting corrections. As usual, I hope that you will enjoy this video.