Lecture Notes on Special Relativity

THE SPECIAL THEORY OF RELATIVITY - Macquarie University

THE SPECIAL THEORY OF RELATIVITY Lecture Notes prepared by J D Cresser Department of Physics Macquarie University July 31, 2003

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Time Evolution in Quantum Mechanics - Macquarie University

Chapter 15 Time Evolution in Quantum Mechanics Physical systems are, in general, dynamical, i.e. they evolve in time.The dynamics of classical mechanical systems are described by Newton’s laws of motion, while the dynamics of the

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Particle Spin and the Stern-Gerlach Experiment

Chapter 6 Particle Spin and the Stern-Gerlach Experiment The spin of an elementary particle would appear, on the surface, to be little different from the spin of a macroscopic object – the image of a microscopic sphere spinning around some axis

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Chapter 6 P article Spin and the Ster n-Gerlach Experiment

Chapter 6 P article Spin and the Ster n-Gerlach Experiment 50 where m e and # e are the mass and char ge of the electron, S is the spin angular momentum of the electron, and g is the so-called gyromagnetic ratio, whic h classically is exactly equal

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Observables and Measurements in Quantum Mechanics

haustive collection of results obtained when measuring some physical property, or observable, of the system. This linking of particular states with particular measured results provides a way that the observable properties of a quantum system can be described in quantum mechanics, that is in terms of Hermitean operators.

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Quantum Physics Notes - Macquarie University

ing of the quantum information aspects of quantum mechanics, and which may perhaps one day finally lead us to a full understanding of quantum mechanics itself. The Language of Quantum Mechanics As mentioned above, quantum mechanics provides a framework into which all physical theories must fit.

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Some Useful Properties of Complex Numbers

Real and imaginary parts The real and imaginary parts of the complex number z= x+ iyare given by Real part Rez= x Imaginary part Imz= y: (1) with Re(az 1 +bz 2) = aRe(z 1)+bRe(z 2) and Im(az 1 +bz 2) = aIm(z 1)+bIm(z 2) (2) where aand bare both real numbers. Complex conjugate The complex conjugate of a complex number z, written

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The Wave Function - Macquarie University

The wave function or wave packet so constructed is found to have essentially zero ampli- tude everywhere except for a single localized region in space, over a region of width 2∆ x , i.e. the wave function Ψ( x , t ) in this case takes the form of a single wave packet, see Fig. (3.3).

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Probability, Expectation Value and Uncertainty

The uncertainty of the observable A is a measure of the spread of results around the mean #Aˆ!. It It is defined in the usual way, that is the difference between each …

  Uncertainty

PHYS201 - Wave Mechanics - Macquarie University

PHYS201 Wave Mechanics Semester 1 2009 J D Cresser jcresser@physics.mq.edu.au Rm C5C357 Ext 8913 Semester 1 2009 PHYS201 Wave Mechanics 1 / 86

Introduction to Modern Physics

Newtonian Physics Developed in the 1800’s, extended forward 200 years. Force and acceleration are related to each other through inertial mass. -Kepler’s laws (accurate for many objects) -Energy is a fundamental quantity that can not be created or destroyed, only transferred. -Mass was recognized as a body’s tendency to resist changes

  Newtonian

THE SPECIAL THEORY OF RELATIVITY

the properties of the physical world is very old: it certainly predates Newton and Galileo, but probably not as far back as Aristotle. What the principle of relativity essentially states is the following: The laws of physics take the same form in all frames of reference moving with constant velocity with respect to one another.

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Lecture Notes on General Relativity Columbia University

di er from each other and lead to radically di erent perspectives for the physical world and its laws. We begin by listing the key assumptions about spacetime in Newtonian physics and then proceed by replacing these assumptions with the postulates of special relativity. 1.1 Newtonian Physics Main assumptions

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General Relativity

the physical world and its laws. We begin by listing the key assumptions about spacetime in Newtonian physics and then proceed by replacing these assumptions with the postulates of special relativity. 1.1 Newtonian Physics Main assumptions The primary assumptions in Newtonian physics are the following 1.There is an absolute notion of time.

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8 Lorentz Invariance and Special Relativity

the Newtonian kinetic energy is obtained at low momentum and that mis the Newtonian mass. At p = 0 we have Einstein’s famous E= mc2! We can easily solve for p in terms of v: v2 c2 = p2 p2 +m2c2, E= mc2 p 1−v2/c2 = γmc2, p = vE c2 = γmv (420) As we shall soon see this modification of the relation between momentum and velocity is

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CHAPTER ONE - NCERT

Newtonian mechanics, till then a very successful theory, could not explain some of the most basic features of atomic phenomena. Similarly, the then accepted wave picture of light failed to explain the photoelectric effect properly. This led to the development of a radically new theory (Quantum Mechanics) to deal with atomic and molecular phenomena.

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MATHEMATICAL MODELING A Comprehensive Introduction

concrete conclusions concerning the world, both natural and artificial, that we live in. 1.1 EXAMPLES OF MODELING Here we do a quick tour of several examples of the mathematical process. We present the models as finished results as opposed to attempting to develop the models. 1.1.1 Modeling with Difference Equations

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Fluid Mechanics 1 034013 Exercise Booklet

1. Ordinary Differential Equations, Differential Operators and Newtonian fluids Ordinary Differential Equations In the last two years of your studies you have taken many basic courses in Mathematics, from Calculus to Partial Differential equations and more. In all of these courses you learned Lemmas and rules and many techniques on

  Newtonian

Classical Dynamics - DAMTP

1.2 Newtonian Mechanics: A Single Particle In the rest of this section, we’ll take a ying tour through the basic ideas of classical mechanics handed down to us by Newton. More details can be found in the lectures on Dynamics and Relativity. We’ll start with a single particle.. A particle is de ned to be an object of insigni cant

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Mass, Energy, the Speed of Light— It’s Not Intuitive!

Newtonian Physics (pre-Einstein) gives good results if the object is moving pretty slowly—less than about 10% of the speed of light (the speed of light is 300,000,000 meters/sec or 186,000 mi/sec). • The mass of an object does not change with speed; it changes only if we cut off or add a piece to the object.

  Newtonian