SF1100 Science Foundation Physics: Quantum Mechanics

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SF1100 Science FoundationPhysics Quantum
Mechanics

• Sow Chorng Haur
• Blk S12 02-15 X 2957
• http/www.physics.nus.edu.sg/physowch/

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Domain of Quantum Mechanics
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Quantum Mechanics (1900-1925)

• Micro-world (e.g. atoms, molecules, electrons)
• Classical physics breaks down
• How do we know? Experimental evidences.

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Important Experiments

• Blackbody Radiation
• Lummer and Pringsheim (1899)
• Photoelectric Effect
• Hertz and Hallwachs (1887-1888)
• Atomic Spectra
• Double-Slits Experiment

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What is Blackbody Radiation?
A cavity whose walls are at a certain
temperature. Atoms composing the walls are
emitting electromagnetic (EM) radiation at the
same time they absorb radiation emitted by other
atoms of the walls. EM radiation occupies the
whole cavity.
At equilibrium, the amount of energy emitted by
atoms amount of energy absorbed. Energy density
of the EM field is constant. A small hole in
the cavity allows the EM wave to escape from the
cavity and be detected in an experiments.
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Blackbody Radiation
This is what one finds in the experiment
This explains the change in color of a radiating
body as its temperature varies
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Ultraviolet Catastrophe

• Ultraviolet radiation has a wavelength that is
  shorter than visible lights
• Classical Physics energy density of
  electromagnetic radiation increases with
  decreasing wavelength.

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Max Plancks Postulate

• Energy of radiation of wavelength lmust be
  discrete and cannot be smaller than hc/l.
  i.e. Energy of radiation E nhc/l
• n integer, c speed of light and h is a new
  fundamental constant of nature
• ( 6.63 x 10-34 Joules sec )

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Blackbody Radiation
Theoretical Prediction
Experimental Measurement
Planck was right !!!
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Photoelectric Effect (PE)

• Many metals emit electrons when irradiated by
  light.

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PE (blue light vs red light)
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PE (bright light vs dim light)

• Higher light intensity ? more electrons emitted.
• But electron maximum kinetic energy remain
  unchanged.

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Einsteins Explanation

• Light consists of particles, called photons
• Each photon has energy E hc/l
• Increase light intensity ? increase number of
  photons.

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Einsteins Explanation

• E W Ek
• E Energy of a photon hc/l
• Ek Kinetic energy of the escaping electron
• W Energy required by an electron to escape from
  a metal. W is known as workfunction
• If E gt W, then electrons will be emitted!

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Einsteins Explanation of PE (Blue light vs Red
light )

• E W Ek
• E hc/l Energy of a photon
• l(blue) 500 nm and l(red ) 650 nm
• Blue light E 4 x 10 -19 J
• Red light E 3 x 10 -19 J
• If W 3.5 x 10 -19 J, then only blue light will
  be able to produce photoelectrons.

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Einsteins Explanation of PE (What about the
effect of light intensity ? )

• E W Ek
• E hc/l Energy of a photon
• More intense light means many more photons, but
  the energy carried by each photon is the same
  since it depends only on its wavelength.
• Hence more intense light will only produce more
  photoelectrons but the maximum kinetic energy of
  the electrons remain the same.
• i.e. Max Kinetic Energy independent of light
  intensity

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Photons

• The wavelength of visible light ranges from 400
  nm to 700 nm. What is the corresponding photon
  energy? (Plancks constant 6.6 x 10-34 Js,
  speed of light 3 x 108m/s)
• (a) 2.83 x 10-19 J to 4.95 x 10-19 J
• (b) 4.95 x 10-19 J to 2.83 x 10-19 J
• (c) 4.95 x 10-28 J to 2.83 x 10-28 J
• (d) 2.83 x 10-28 J to 4.95 x 10-28 J
• (e) 1.65 x 10-27 J to 9.43 x 10-28 J
• Answer (b) (Use E hc/l)

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Separating Lights
From Online Journey Through Astronomy (OJTA)
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Atomic Spectra

• Evacuated glass tube filled with hydrogen gas.
• When an electrical discharge is passed through
  the gas, light will be emitted and its colour is
  characteristic of the gas.

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Atoms energy quantized too

• The energy of an atom can have only certain
  values E1, E2, E3, (energy is quantized)
• The states corresponding to these energies are
  called stationary states and the possible values
  of energy are called energy levels.
• Emission of light results in a transition of the
  atom from one stationary state to another of
  lower energy.

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Radiative Transitions
Say an atom went from state with energy E2 to the
ground state with energy E1. The difference in
energy is released as photon with energy
E2-E1. Energy of Photon is E hc/l hc/l
E2-E1 The wavelength of photon (I.e. the color of
light) is the signature of the transition as well
as the atom itself.
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Energy Levels Animation

• http//www.colorado.edu/physics/2000/applets/schro
  edinger.html

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Absorption Spectrum of the Sun

• Absorption spectrum of the Sun
• We can probe the constituent elements of the sun
  from a distance!

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Double-Slit Experiment (I)

• Using bullet to illustrate particle behavior

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Double-Slit Experiment (II)

• Using water wave to illustrate wave behavior

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Double-Slit Experiment (III)

• How about electrons? Are they particle or wave?

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Double-Slit Experiment (IV)

• Electrons Wave-like Property

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Double-Slit Experiment

• See Animation of Electrons Wave-like Property
• http//www.Colorado.EDU/physics/2000/applets/twosl
  itsa.html
• http//www.Colorado.EDU/physics/2000/applets/twosl
  itsb.html

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Wave-Particle Duality

• Light sometimes behaves like particles
• Photoelectric effect
• Particles sometimes behave like waves
• Double-slit experiment with electrons and atoms.
• Wave Packet

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Louis de Broglies Equation

• Wavelength of a particle
• Relate particle-like property (momentum p) to
  wave-like property (wavelength l )
• l h/p

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de Broglies wavelength example

• l h/p
• p mass (m) x velocity (v)
• For a basketball, m 1 kg, v 1 m/s
• de Broglie l 6.63x10 -34 m
• For an electron, m 9x10 -31 kg, v 1 m/s
• de Broglie l 7.29x10 -4 m

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de Broglies wavelength

• Which of the following statements does not follow
  from wave-particle duality?
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• (a) Light sometimes behaves like particles.
• (b) Particles sometimes behave like waves.
• (c) Electrons exhibit an interference effect in
  the double-slit experiment.
• (d) The larger the momentum of a particle, the
  longer its de Broglie wavelength will be.

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Heisenbergs Uncertainty Principle

• Suppose we know x really, really well. Then we
  cannot know p very well. And vice versa.
• Dx Dp ? h/2p
• The act of measurement changes
  the system.

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Heisenbergs Uncertainty Principle

• Any measurement made will satisfy the uncertainty
  relation and be of only a limited precision.
• The classical concept of having an arbitrarily
  precise knowledge of both x and p does not hold
  in the micro-world.

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Heisenbergs Uncertainty Principle

• In a certain experiment, the position of an
  electron is determined to an accuracy of Dx 10
  9 m. Assuming that the electron is
  non-relativistic, what is the most accurate
  knowledge we can hope to have about its velocity
  in this experiment?
• Dx Dp ? h/2p and Dp m Dv . We have
• Dv ? h/2mp/ Dx where
• Planck constant h 6.6x10-34 Js
• mass of electron m 9.1 x 10-31 kg and
• Dv ? 1.16 x 10 5 m/s

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QM Description of Micro-world

• What happen when we do not make any measurement
  to determine the position or the momentum of a
  particle?
• Does it have a definite position or a definite
  momentum?
• No, particle is in a probabilistic state, both
  position and momentum have a likelihood of having
  a range of values.

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Wave Function

• Wave Function Y(x,t) describes a particle
• The quantity Y2 is interpreted as the
  probability that a particle can be found in a
  particular region in space and at a particular
  time

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Schrodingers Equation

• Schrodingers equation
• Analogue of Newtons Equations in Classical
  Mechanics.