Physics Lecture 7 2/16/ Andrew Brandt Monday February 16, 2009 Dr. Andrew Brandt 1.Wave Properties of Particles 2.de Broglie Waves 3.Matter Waves 4.Wave Equation

De Broglie Waves Particle properties of waves supported by data De Broglie in the 1920’s made a bold proposal without strong evidence that moving particles could have wavelike properties (Nobel Prize when verified) [Rubbia] Photon: De Broglie suggested that this is a general expression, so for a relativistic particle with this implies that. This is the general expression for the de Broglie Wavelength Large momentum implies short wavelength (accelerators with large momentum thus probe short wavelengths/small distances; ex. search for compositeness) Wave and particle aspects cannot be observed at the same time. Which properties are most evident depends on how the compares with particle’s dimensions, and the dimensions of what the particle interacts with 2/16/ Andrew Brandt2

De Broglie Example 3.1 Tiger says to his caddie, “I wonder if my golf ball has wavelike properties? He hits a 46 g golf ball with a velocity of 30 m/s (swoosh). Find the ; what do you expect? The wavelength is so small relevant to the dimensions of the golf ball that it has no wave like properties What about an electron with ? This large velocity is still not relativistic so Now, the radius of a hydrogen atom (proton + electron) is Thus, the wave character of the electron is the key to understanding atomic structure and behavior 2/16/ Andrew Brandt3

De Broglie Example 3.2 2/16/ Andrew Brandt4 What is the kinetic energy of a proton with a 1fm wavelength Rule of thumb, need relativistic calculation unless This implies a relativistic calculation is necessary so can’t use KE=p 2 /2m

What kind of wave is it? Sound waves are waves of pressure, light waves are EM fields, what are dB Waves? Matter waves: the wave function (sigh) is related to the likelihood of finding a particle in a place at a certain time Although the wave function itself has no physical significance, (the square of the absolute value of the wave function represents the probability density: the probability of experimentally finding a body described by the wave function at a given point (x,y,z) at a given time t is proportional to If this is non-zero, then there is a chance to find the particle in that place The wave function describes the particle as spread out in space, but the particle itself is either found at a certain time or place … or not You can’t find 20% of an electron, but you can have Calculating this wave function is the purview of Quantum Mechanics (Ch. 5+6) 2/16/ Andrew Brandt5

Phase Velocity How fast do dB waves travel? Might guess wave has same velocity as particle One speed associated with a wave is the phase velocity We have an expression, but what’s nu? so Thus ! Oops, with v<c this means that, so phase velocity cannot be correct speed of particle represented by de Broglie waves. 2/16/ Andrew Brandt6

Wave Equation 2/16/ Andrew Brandt7