Download Quantum Mechanics I. Introduction Just before 1900, the classical

Quantum Mechanics
I. Introduction
Just before 1900, the classical physics of Newton and Maxwell was unable to explain
certain phenomena. The result was a major revolution in physics, the development of
quantum mechanics. We no longer see the world as precisely definable, but there is an
inherent uncertainty and fuzziness to nature. The uncertainty principle and
particle/wave duality play a fundamental role in our current understanding.
http://www.youtube.com/watch?v=45KGS1Ro-sc
II. Blackbody Radiation
A. In physics, a black body is an
idealized object that absorbs all
electromagnetic radiation falling on
it and then re-emits it in a
characteristic pattern called the
blackbody spectrum.
B. Accelerated charged particles emit
electromagnetic radiation. The
thermal oscillation of molecules in a
substance results in the emission of radiation. Since all objects have some
temperature, all objects emit radiation.
C. Classical theory, modeling the atoms as harmonic oscillators, resulted in the
“ultraviolet catastrophe”. Max Planck, in order to reproduce the experimental
results, had to assume that each oscillator could only have an integral number of
units of energy, rather than have any arbitrary amount. In other words, the
energy of each oscillator was quantized.
D. Planck saw this quantization as purely a mathematical trick to get the theory to
fit the data. However, Albert Einstein in 1905 suggested that this quantization
wasn’t just a trick, but that light came in packets, now called photons
E. Planck won the Nobel Prize in Physics in 1918 and Einstein won it in 1921.
III. Quantization of Energy
A. The energy of a single photon is given the equation:
where h is known as Planck’s constant and has the value 6.63×10−34 J s.
B. Example: What is the energy of a single photon of green light ( = 540 nm)?
IV. Atomic Spectra
A. Atomic spectra emission lines are a result of
electrons moving from a higher to a lower
energy level in the atom.
where c is the speed of light = 3.00 x 108 m/s
and  is the wavelength of light.
B. Example: What is the wavelength of light in nanometers for the n = 3 to n = 2
transition in hydrogen? (En=3 – En=2 = 3.03 x 10-19 J)
V. Wave-Particle Duality
A. In 1924, Louis de Broglie proposed the idea that just as light has both wave-like
and particle-like properties.
B. Example 1: What is the momentum of a single photon of 400. nm light?
C. Example 2: What is the wavelength of an electron moving at 1.00 x 104 m/s in
nanometers? (me = 9.11 × 10-31 kg)
VI. Uncertainty Principle
A. In 1926, Werner Heisenberg formulated the uncertainty principle.
Video: http://www.youtube.com/watch?v=KT7xJ0tjB4A
B. Example 1: What is the minimum uncertainty in the position, x, of an electron
if the uncertainty of its velocity, v, is 2.00 cm/s?
C. Example 2: What is the maximum time a virtual electron-positron pair (note:
positron = anti-electron) can pop into existence out of the vacuum and not
violate the uncertainty principle? (E = mc2)
VII. Double-Slit Experiment
A. Quantum Man Explains
http://www.youtube.com/watch?v=wEzRdZGYNvA&feature=related
B. Neon atoms – one at a time
http://www.youtube.com/watch?v=GdnL_S4qdTU&feature=related