Origins The of the Quantum Theory Planck (1900) E=h
o
Data Theory
Einstein (1905)
o Data
Bohr (1911)
Emax
Slope = h
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Phys 199EPP Lecture 3
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QM: Esoteric or Relevant?
Quantum mechanics provides for some fun discussions on abstract topics.
Schrodinger's cat, Many worlds, role of the observer...
But is it relevant in "the real world"?
Absolutely.
Estimate that quantum mechanics accounts for about 1/3 (~$3T) of the U.S. gross national product (USGNP ~$10T) Examples:
Lasers Nuclear power Integrated circuits MRI (NMR) Superconductivity Light emitting diodes Active solar power Anything with chemistry ...
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Phys 199EPP Lecture 3
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Timeline "Modern Physics"
Einstein Bohr Michelson Rutherford Thomson De Broglie Planck Schrodinger Curie Heisenberg 1900 Special Relativity Nuclear Energy Neutron Stars Released discovered 2000
1950 Expansion Laser of Universe Invented discovered Transistor Invented
Start of Quantum Quantum General Mechanics Relativity Mechanics
All the Quarks discovered
Last time: relativity Today: quantum mechanics
31-Jan-06 Phys 199EPP Lecture 3 3
Atoms
Quote from the famous modern physicist, Richard Feynman:
If we were able to pass along only one bit of scientific knowledge to future generations, what would be the most important one piece of information to choose?
Feynman's answer:
That matter is made of atoms
What could this mean? How could this fact be so important?
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Phys 199EPP Lecture 3
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The Appeal of Atomism
It is natural to try to explain the vast diversities that we see in terms of the arrangements and interactions of a small number of fundamental building blocks: atoms! Atomism in Ancient Greece:
Democritus: There are only atoms and the void. Apparent qualities are result of shape, arrangement, and position of atoms. Atoms remain unaltered.
Gave us the name: atom - "indivisible"
Explains the basic properties of matter
Changes but is never created nor destroyed (in our ordinary experience)
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The Periodic Table
Question: Do the properties of atoms (elements) indicate that there are more than 100 different flavors of these "fundamental" pieces? Or do the properties indicate a pattern of substructure??
Atomic # = # of protons
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Are Atoms Indivisible?
"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 Xrays) given off from ore containing Uranium.
Marie Curie (1897) discovers immense radiation energy from element she named Radium.
Surprising? Yes!
If the radiation comes from the atom, it could indicate that an atom had been transformed into another kind of atom! If atoms are not immutable, then it makes sense to ask "what are atoms made of?"
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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").
Blackbody Radiation
frequency
31-Jan-06 Phys 199EPP Lecture 3 8
Planck's Solution
Max Planck (1901): In order to describe the data Planck made the bold assumption that light is emitted in packets or quanta, each with energy E = h, where is the frequency of the light. The factor h is now called Planck's constant, h = 6.626 x 10-27 erg-sec.
o
Data Theory
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E = h
The two most important formulas in modern physics
E = mc2 (Einstein special relativity - 1905) E = h (Planck quantum mechanics - 1901)
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
31-Jan-06 Phys 199EPP Lecture 3 10
Photoelectric Effect
Einstein took Planck's hypothesis seriously in order to explain the photoelectric effect. Effect: Shining light on a metal can liberate electrons from its surface. Experimental facts: Easy for UV light (high frequency) hard for red light (low freq). Energy of the electrons depends on frequency of light Increasing intensity of light increases number of electrons emitted, but not the energy of each electron Can't be explained by "wave" behavior of light. If light is generated in quantized units, Einstein reasoned it would also arrive with quantized amounts of energy
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Phys 199EPP Lecture 3
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Light is Quantized!
We referred to light as a wave. Blackbody radiation and the photoelectric effect indicate that the energy transmitted by light comes in packets!!
Light doesn't behave like a wave. The energy light carries is quantized, which means it comes in tiny bursts. The amount of energy per burst is determined by the frequency and Planck's constant h:
E=h
Light can behave like a particle. Any chance a particle can behave like a wave?
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Phys 199EPP Lecture 3
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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 below; x
source detector
The Two-Slit Experiment
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.
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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 at deposited 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).
Classical Particles
only bottom slit open
only top slit open
N
N
Both slits open
x
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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.
Classical Waves
Interference
only bottom slit open only top slit open
Both slits open I
I
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Phys 199EPP Lecture 3
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Quantum Mechanics
Particles act like waves! Experiment shows that particles (like electrons) also act like waves!
only bottom slit open only top slit open
Both slits open I
I
x
x
31-Jan-06
Phys 199EPP Lecture 3
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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?
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Phys 199EPP Lecture 3
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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!
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Towards Understanding
Bohr atom
Quantized energy levels, allowed orbits
deBroglie waves
Particle acts like wave, wavelength depends upon momentum
Obviously related, but unclear exactly how... Erwin Schroedinger pulled it all together in 1926
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The Schrodinger Equation
In 1926 Erwin Schrodinger proposed an equation which describes completely the time evolution of the matter wave :
( - (h2 / 2m) 2
+ V) = i h (d /dt)
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)
Schrodinger
Given potential, find wave
(- (h2 / 2m) 2
solution: x = f(t)
solution: = f(x,t)
+ V) = i h (d /dt)
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 .
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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.
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Phys 199EPP Lecture 3
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What is ?
Our current view was fully developed by Bohr from an initial idea from Max Born. Born's idea: is a probability amplitude wave! 2...