• quantum mechanics is generally perceived as a topic that is limited to
    • particle scientists
    • philosophers

  • with no bearing on commercial applications

  • however, this has ceased to be true
    • quantum mechanics is used routinely in engineering
    • much of the modern world engineering
  • measurement problem
    • the glitch in the philosophy of quantum mechanics
  • despite this, it is allegedly easy to use
    • it works even if not understood very well

light

  • quantum mechanics is obvious
  • classical mechanics has no theory about why objects are the colors they are
  • a problem with color is what triggered the exploration of quantum mechanics

kirchoff’s law of thermal radiation

  • if something absorbs all radiations it is subjected to
  • then when it is heated up, it would best emit thermal radiation, compared to other alternatives

  • the best possible absorbers are best emitters when heated up and hence they are called blackbody

  • the power of sunlight is relatively uniform per unit wavelength across its emission spectrum

black-body spectrum**: output power (per unit wavelength)

  • for a black body at 5800K, approx. like the sun

  • for a black body at 3000K, approx. like an incandescent bulb

  • a filament bulb however does not have a uniform power distribution across it’s spectrum
    • it peaks at a particular short wavelength

ultra-violet catastrophe

  • the rayleigh-jean model for filament black body spectrum fails to predict the spectrum for shorter wavelengths

Rayleigh-Jean vs Experimental

wien’s displacement law

  • predicts blackbody spectrum at lower wavelengths but failed at higher wavelengths

max-plank’s curve fitting

  • fit a mathematical model to the experimental black body spectrum

  • empirical model, not based on fundamental physics
    • pulled a constant out of his arse to fit the curve
  • this pulling numbers out of his arse marked the start of quantum mechanics
    • when he presented the numbers pulled out of his arse to a bunch of euro trash and other wieners in early 1900
  • certain assumptions went into pulling the constant out of his arse
    • light is emitted in chunks of an amount proportional to its frequency
  • \( E = h\nu \)
    • \( \nu \): frequency of light (in \(Hz\) )
    • \( h \): planck’s constant = \( 6.625 X 10^{-34} Js \)

  • plank’s constant is the number plank pulled out of his arse to fit his curve to the measured black body spectrum

  • he proposed that light travelled as waves, but black bodies emit these as chunks
    • no explanation given as to why, so he had to come up with a constant out of his arse
    • the corpuscles model existed earlier (1600) i.e. the light was made of particles

photoelectric effect

  • experiment by heinrech hertz:
    • put voltage between metal plates
    • shine ultraviolet light on one of them
    • spark between the plates become brighter
    • the light they shone on these pieces of metal has to be UV
    • if glass is put in front of light, the sparking effect stopped
  • philip lenred said this experiment gives flow of negative charge
    • if the plates were in a vacuum and a light was shined on them
    • when biased with an electric current to offset the induced current, the kinetic energy of the negative charge was deduced
    • when the frequency of the light increased, the stopping voltage to generate the offset current increased
  • photons approach by einstein
    • he said the chunks have the energy of \(h\nu\)
  • work function \(\phi\): energy barrier for electrons to overcome to be released from the metal lattice
    • when energy of electron \(h\nu > \phi\) because of incident light, it is released from the metal lattice, and excess energy is converted to kinetic energy
    • the stopping electric potential energy can oppose this kinetic energy
    • this is why einstein was awarded nobel prize, not general relativity theory

wave-particle duality

  • light is allegedly simultaneously a wave and a particle
    • arguably not a problem in quantum mechanics
    • but the paradigm of classical attributes of particles and waves has to be turned a blind eye to
      • only some properties are valid in quantum mechanics

interference and superposition

  • interference effects appear in various different ways in different quantum mechanical situations
  • in a quantum mechanical superposition, you add the amplitudes first and then take the modulus squared of the sum to get the probabilities

  • there is no analog to that process in the classical view of particles and particle states

  • though superposition and interference are not really meaningful ideas for classical particle, superposition and interference do occur all the time with classical waves
    • that is one reason why it is useful to understand classical waves as we begin to look at quantum mechanics.

optical-fiber communication

  • verifies wave-particle duality trillions of times a day
  • the fibers are hair-thin pieces of glass
    • designed based on wave nature of light, using maxwell’s equations and 19th century physics
  • the devices that generate the light beams i.e. lasers, and the devices that detect these light beams at the end of the glass tunnel i.e. photodetectors are both quantum mechanical devices
    • they generate photons and detect photons respectively
    • trillions of bits of information are sent over the internet everyday
    • the framework for modern day networks
  • map of the internet
  • telecom maps