Introduction to Quantum Physics

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Introduction to Quantum Physics

• Early Atomic Physics

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What is Quantum Physics

• Quantum Physics is a collection of laws which
  explain observations of the tiny building blocks
  of all matter.
• The world of the quantum must be able to explain
  the classical world that we live in.
• To understand the quantum world we need to
  understand one of the major building blocks ----
  the atom

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History of Atomic Structure

• The model of atomic structure has changed as
  observations have altered our perceptions
• Democrictus
• Dalton
• Thomson
• Rutherford
• . (The model is not complete)

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Democritus

• Atoms (Greek for indivisible) are the smallest
  unit of matter
• Atoms share all of the properties of the
  macroscopic object
• Atoms are the smallest pieces of matter which
  still act as the material from which they come
  from

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John Dalton

• First truly scientific theory of the atom
  (results discovered through experiments with
  marsh gases)
• Proof of early Greek model --- the atom is
  indivisible but with no internal structure
• Properties of matter come
• from the properties of the atom

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• But what about electricity?

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J.J. Thomson

• Discoverer of the electron
• The atom consists of a positively charged
  substance (like pudding) containing negative
  charges (like the raisins in a plum pudding)

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Rutherford

• 1909 Rutherford performs an experiment in which
  alpha particles (He nucleus) are fired towards a
  thin foil of gold

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Rutherford

• Experimental observations indicated that the
  majority of the alpha particles passed straight
  through, with few being deflected at small angles
  and even fewer retro reflecting from the gold foil

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Rutherford

• Observations indicate that the atom is mostly
  empty space with a dense, central,
  positively-charged structure at its center
• The electrons (discovered by Thomson) must
  therefore exist outside of this central nucleus
  . Orbiting around the nucleus as planets do the
  Sun.

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Classical Model

• The Rutherford model of the atom became known as
  the classical model of the atom

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Problem with the classical Model

• The Theory
• The electron has a negative charge and orbits
  about the central nucleus
• The central nucleus has a charge and therefore
  must also have a magnetic field
• Charged particles lose energy as they pass
  through a magnetic field
• According to classical electro-magnetic theory
  the electron should lose energy in its orbit.

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• Observations
• The atom is a stable structure consisting of sub
  atomic particles that do not normally decay in
  our life time.
• Because the observation does not match the theory
  . either classical physics is wrong OR the
  Rutherford model is wrong / incomplete

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• Which is easier to believe ?
• Hundreds of years of Physics laws and theories
  are wrong.
• A relatively new model of our atom is wrong.
• Answer
• Both classical physics and the Rutherford model
  have some minor problems.
• But it is our picture of the atom which is mostly
  incorrect.

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Enter Niels Bohr

• Bohr succeeded in solving the problem with the
  classical model by uniting two disparate ideas
  Plancks quanta and the hydrogen emission spectra

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Max Planck

• Observed the temperatures of cannons as they were
  bored out
• The colour of the emitted
• radiation is related to the
• temperature of the cannon
• The expected peak intensity follow the
  Rayleigh-Jean
• law

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Rayleigh-Jean Law
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Ultraviolet Catastrophe

• The classical (Rayleigh-Jeans) model predicted a
  steady increase in Intensity well into the
  ultraviolet
• If the theory worked with
• the cannons then enough
• ultraviolet radiation would
• be emitted to destroy life.

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Energy is not continuous

• Planck solved the catastrophe by re-imagining
  Energy
• Energy is not a continuous stream but consists of
  chunks or discrete packets
• Energy is quantized (flows as quanta)

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• Planck did not initially believe in his findings
• Why would energy be quantized it is neither
  simple or beautiful
• Plancks findings were instrumental in the work
  for which Einstein won the Noble Prize in Physics
• Photoelectric Effect

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Quanta of Energy

• Vibrating molecules can only vibrate with certain
  discrete amounts of energy
• Each quanta of energy can be determined by E hf
• E is the energy of the Quanta (J or eV)
• f is the frequency of the vibration
• h is Plancks constant (6.626 x 10-34 Js)

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Hydrogen emission spectra

• Bohr also received a clue from the emission
  spectra of the Hydrogen atom
• Again the classical model predicts that the atom
  should be able to radiate in an infinite range of
  wavelengths but observations indicate otherwise

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Energy is quantized

• If the electron in the atom can only absorb or
  emit discrete quantities of energy (quanta) then
  the emission spectra makes sense
• By using Plancks hypothesis and the clues from
  the emission spectra of Hydrogen Bohr was able to
  mathematically explain the nature of the atom

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Hydrogen emission spectra
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Bohrs theory

• Bohrs theory was the first step in the Quantum
  revolution
• Postulate of Stationary States the Hydrogen
  atom can exist, without radiating energy, in any
  one of a discrete set of orbits of fixed energy
• Frequency Postulate the Hydrogen atom can emit
  or absorb a quantity of energy only when the
  electron changes from one stationary state into
  another. This amount can be calculated by Ehf

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Question

• How does the concept of the quantization of
  energy circumvent the problem with the classical
  model?

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The Atom so far .

• A central nucleus (of positive charge) is
  surrounded by negatively charged particles called
  electrons
• Electrons can only orbit in fixed distances from
  the nucleus because they can only gain / lose a
  quanta of energy
• This prevents the electron from falling into
  the nucleus

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Problems with the Bohr model

• The two postulates only work with the Hydrogen
  atom. When the model is applied to other atoms
  extra dimensions of space is required.

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• The works of Grimaldi have shown that electrons
  are capable of displaying an interference
  pattern. How could a particle do this?
• Both of these problems can be solved to create
  a new theory by applying the works of deBroglie
  and Schrodinger.

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Louis de Broglie

• First degree in History but applied for graduate
  work in Physics
• Doctoral thesis Recherches sur la théorie des
  quanta 
• Work beyond the intellect of his professors
• Sent to Einstein who endorsed it fully

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Matter Waves

• De Broglie proposed that all matter have both
  matter properties and wave properties.
• Start with the Einstein energy-matter equality
• E mc2
• This energy is quantized according to Planck
• So E hf mc2

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• hf mc2
• hf (mc)c
• mc is the momentum of the wave p
• hf pc
• v fl
• hf p(fl)
• h pl
• So p h / l

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• In short any piece of matter travelling at any
  speed can exhibit wave properties
• The effects for classical particles are too small
  to observe
• The electron is not only a particle but also
  displays wave nature
• Therefore the electron can diffract
• Light also displays both particle and wave nature

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Bohr model revision 1

• The atom consists of
• A massive positively charged central nucleus
• Negatively charged electrons which create
  standing waves of energy.
• These waves of energy can only vibrate / resonate
  at specific frequencies
• These frequencies determine the orbitals around
  the nucleus
• de Broglie matter waves do not solve the
  multi-dimensionality problem!

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Enter Schrodinger

• Einstein given the task to apply the Bohr/de
  Broglie model to atoms other than Hydrogen
• Was too busy working on GUT so he passed the task
  on to his friend Erwin Schrodinger
• Schrodinger was an unpopular choice in that he
  was considered a failed Physicist!

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• Christmas holidays and New Years 1925-26
• Schrodinger takes his mistress into the Alps on
  vacation
• It is here that he comes up with his wave
  equation for all matter
• This set of equations works for all atoms --- not
  just Hydrogen

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The Schrodinger wave model
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• de Broglies matter waves do not describe the
  physical location of the electrons around the
  nucleus
• The mathematics describes the probability of
  finding the electron in a given location of space
• Loss of determinism?!?!?
• All life is based on probability there are no
  definite knowns!

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• God does not play dice with the Universe

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Implications of a Probabilistic Universe

• Quantum tunneling
• HUP
• Schrödinger's cat
• BEC
• Separation of classical world and quantum world

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Quantum Tunneling

• Imagine that you have a single electron that you
  place into an electrical potential well. The
  electron requires an infinite amount of energy to
  climb out of the box.
• Where is the electron?

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• Now imagine that you leave the electron and
  return to it a few weeks later.
• Where is the electron now?

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• Classical Physics would tell us that the electron
  must always be in the electropotential well
  since it doesnt have enough energy to climb
  out
• Experimental evidence indicates that the electron
  will leak out over time!!!
• This is the process through which semiconductors
  work

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• The Schrodinger equation defining the position of
  the electron is both energy, and time dependent
• As time proceeds the probability of finding the
  electron in a set location begins to smear out
  over space.
• There is a probability that the electron can
  climb out of the electropotential well.

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Heisenbergs Uncertainty Principle

• Two versions of HUP
• Uncertainty between knowing the momentum of an
  object and the exact position of an object
• Uncertainty between knowing the amount of energy
  a substance contains within a time interval of
  measurment

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Momentum and position

• Imagine that we have a small sub atomic particle
  that we want to observe and record all possible
  data for.
• We start to attempt to measure the momentum of
  the object
• To measure the velocity (and therefore the
  momentum) we need to set up a set of timing gates

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• We can use low energy x-rays to record the
  passage of the sub atomic particle from one gate
  to the other
• This will allow us to measure the velocity and
  therefore the momentum
• The wavelength of the x-ray is too long at low
  energies so even though we can use it to measure
  the momentum we can not use it to determine the
  exact position.

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• We can increase the energy of the x-ray which
  results in a tighter wavelength
• This will allow us to know the exact location of
  our subatomic particle
• But the increase in energy imparts energy to our
  sub atomic particle changing its motion
  direction . And therefore changing the momentum

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• So
• By measuring the momentum the exact position
  remains unknown
• By measuring the exact position we change the
  momentum
• We can not know the exact position and momentum
  at the same time.
• A similar uncertainty exists between energy and
  time

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Schrodingers Cat

• The macroscopic / classical physicists rebuttal
  to HUP
• Classical physicists refuse to believe that
• It is impossible to know everything about a
  system
• The act of observing a system changes the system
  ... The act of experimentation destroys
  determinism