Download Document

A BRIEF STORY OF QUANTUM THEORY
PETER BALLO
END OF 19th CENTURY
Classical Mechanics
Electromagnetism and Optics
Heat
State of Physics at 1895
•Lord Kelvin—arguably the
greatest physicist of his day:
• Strong opponent of existence of atoms
•“There is nothing new to be discovered in
physics now. All that remains is more and more
precise measurement."
•Albert A Michleson—the first US
Physics Nobel laureate
•“The grand underlying principles have been
firmly established...further truths of physics are
to be looked for in the sixth place of decimals"
(Science, 1892)
Hydrogen Spectrum: Balmer series
Balmer Formula:
IT WORKS!
• “X-rays” discovered in 1895 by Roentgen
- World Wide sensation!
– Unknown ray produced from electric
discharge that penetrates matter!
• J.J. Thomson discovers the electron in
1897.
• Henri Becquerel (1896) tries to produce
X-rays from natural sources.
– Finds radiation (less penetrating
than X-rays) given off from solid
containing Uranium.
• Marie Curie (1897) discovers immense
radiation energy
from element she named Radium.
–
Surprising? Yes!
Black body radiation
Otto Lummer
Ernst Pringsheim
Blackbody Radiation Spectra
• The true beginnings of the quantum theory lie in a strange place:
the frequency spectrum emitted by a solid when it is heated
(“blackbody” radiation).
• Experimental measurements: the frequency spectrum was well
determined.. a continuous spectrum with a shape that depended
only on the temperature (light bulb, … )
• Theoretical prediction: Classical kinetic theory predicts the energy
radiated to increase as the square of the frequency (Completely
Wrong! - “ultraviolet catastrophe”).
Planck’s Solution
• Max Planck (1900): In order to describe the data
Planck made the bold assumption that light is emitted
in packets or quanta, each with energy
E = h f, where f is the frequency of the light.
– Some texts use the notation n for frequency.
• The factor h is now called
Planck’s constant, h = 6.626 (10-27) erg-sec.
o
Data
Theory
Atomic Models
• Conclusion: Atoms contain electrons.
Questions: How are they arranged? Since
atoms are neutral, where is the positive charge?
• Two models:
–“Plum pudding”: Electrons are embedded in
continuum of positive electricity like plums in a
pudding.
–“Planetary model”: Electrons orbit a small nucleus of
positive charge like planets orbit the Sun.
Electrons
Or
Positive Charge
probe
probe
For plum pudding: expect
only small angle scattering.
For planetary model: may
see small angle or large
angle scattering.
Rutherford saw
large angles…
planetary model!
The Problem of the atom
• Experiments supported the picture that an atom is
composed of light electrons around a heavy nucleus
• Problem: if the electrons orbit the nucleus, classical
physics predicts they should emit electromagnetic
waves and loose energy.
If this happens, the electrons
will spiral into the nucleus!
• The atom would not be stable!
• What is the solution to
this problem?
E=hf
Bohr’s Revolutionary Idea
• Can the new quantum theory
explain the stability of the atom?
• If the energies can take on only
certain discrete values, i.e., it is
quantized, there would be a lowest
energy orbit, and the electron is
not allowed to fall to a lower
energy!
• What is the role of
Planck’s Constant h?
The Bohr Atom
(NOT Correct in detail!)
4
•
The allowed orbits are labeled by the integers: n =
1, 2, 3, 4.
•
The radii of these orbits can be determined from
the quantization condition:
radius = n2 a0 = n2 (h/2p)2/ me2
•
The energy can only have the values En= E1 /n2,
E1 = - (1/2)(e2 / a0)/n2
•
The spectra are the result of transitions between
these orbits, with a single photon (f = E/h)
carrying off the difference in energy E between
the two orbits.
3
2
1
The Schrodinger Equation
• In 1926 Erwin Schrodinger proposed an
equation which describes completely the time
evolution of the matter wave 
where m = characteristic mass of “particle”
V = potential energy function to describe the forces
Newton:
Given the force, find motion
F = ma = m (d2x/dt2)
solution: x = f(t)
Schrodinger
Given potential, find wave
(- (h2 / 2m) 2
+ V)  i h (d /dt)
solution:  = f(x,t)
Note: Schrodinger’s equation is more difficult to solve, but it is
just as well-defined as Newton’s. If you know the forces acting,
you can calculate the potential energy V and solve the
Schrodinger equation to find .
Key Results of Schrodinger Eq.
• The energy is quantized
–Only certain energies are allowed
–Agrees with Bohr’s Idea in general
–Predicts the spectral lines of Hydrogen exactly
–Applies to many different problems - still one of the
key equations of physics!
• The wavefunction is spread out
–Very different from Bohr’s idea
–The electron wavefunction is not at a given radius
but is spread over a a range of radii.
Probability interpretation for 2
• The location of an electron is not determined by
. The probability of finding it is high where 2
is large, and small where 2 is small.
• Example: A hydrogen atom is one electron
around a nucleus. Positions where one might
find the electron doing repeated experiments:
Lower probability
to find electron
far from nucleus
Higher probability
to find electron
near nucleus
Nucleus
The Two-Slit Experiment
• We will first examine an experiment which
Richard Feynman says contains “all of the
mystery of quantum mechanics”.
• The general layout of the experiment consists of
a source, two-slits, and a detector as shown
x
below;
source
detector
slits
The idea is to investigate three different sources (a classical particle
(bullets), a classical wave (water), and a quantum object (electron or
photon)). We will study the spatial distribution (x) of the objects which
arrive at the detector after passing through the slits.
Classical Particles
• Classical particles are emitted at the source and arrive at the detector only if
they pass through one of the slits.
• Key features:
– particles arrive “in lumps”. ie the energy deposited at the detector is not
continuous, but discrete. The number of particles arriving per second
can be counted.
– The number which arrive per second at a particular point (x) with both
slits open (N12) is just the sum of the number which arrive per second
when only the top slit is opened (N1) and the number which arrive per
second when only the bottom slit is opened (N2).
only bottom
slit open
only top
slit open
Both slits
open
N
N
x
x
• Classical waves are emitted at the source and arrive at the detector only if they
pass through the slits.
• Key features:
– detector measures the energy carried by the waves. eg for water waves, the
energy at the detector is proportional to the square of the height of the wave
there. The energy is measured continuously.
– The energy of the wave at a particular point (x) with both slits open (I12) is NOT
just the sum of the energy of the wave when only the top slit is opened (I1) and
the energy of the wave when only the bottom slit is opened (I2). An interference
pattern is seen, formed by the superposition of the piece of the wave which
passes through the top slit with the piece of the wave which passes through the
bottom slit.
only bottom slit open
only top slit open
Both slits open
I
I
x
x
Timeline - Modern Physics
Einstein
Bohr
Michelson
Rutherford
Thomson
De Broglie
Planck
Schrodinger
Curie
Heisenberg
1900
Special
Relativity
Start of
Quantum General
Mechanics Relativity
Nuclear Energy
Neutron Stars
Released
discovered
1950
Expansion
Laser
of Universe
Invented
discovered
Quantum
Mechanics
Transistor
Invented
2000
All the
Quarks
discovered
• “Modern Physics” was a sudden revolution starting
around 1900, and ending ????
“Thirty Years That Shook Physics”
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
1887 Michelson-Morley exp. debunks “ether”
1895 Rontgen discovers x rays
1897 Becquerel discovers radioactivity
1897 Thomson discovers the electron
1900 Planck proposes energy quantization
1905 Einstein proposes special relativity
1915 Einstein proposes general relativity
1911 Rutherford discovers the nucleus
1911 Braggs and von Laue use x rays to determine crystal structures
1911 Ones finds superconductors
1913 Bohr uses QM to explain hydrogen spectrum
1923 Compton demonstrates particle nature of light
1923 de Broglie proposes matter waves
1925 Davisson & Germer prove matter is wavelike
1925 Heisenberg states uncertainty principle
1926 Schrodinger develops wave equation
1924-6 Boson and Fermion distributions developed
•
1949 Murphy's Law stated
• The two most important formulas in modern physics
• E = mc2 (Einstein – special relativity - 1905)
E = h f (Planck – quantum mechanics - 1900)
• Planck initially called his theory “an act of desperation”.
– “I knew that the problem is of fundamental significance for
physics; I knew the formula that reproduces the energy
distribution in the normal spectrum; a theoretical
interpretation had to be found , no matter how high.”
• Leads to the consequence that light comes only in certain
packets or “quanta”
• A complete break with classical physics where all physical
quantities are always continuous