Download Quantum Mechanics Lecture 1 Dr. Mauro Ferreira

Quantum Mechanics
Lecture 1
Dr. Mauro Ferreira
E-mail: [email protected]
Room 2.49, Lloyd Institute
Course prerequisites:
It is assumed that you have a working knowledge of
fundamental mathematical methods.
lly
• Calculus;
• Complex variables;
• Linear algebra
• Differential equations
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• Additional tools will be introduced
Furthermore ...
• Classical mechanics;
• Electromagnetism;
• Introductory Modern Physics;
Objectives:
By the end of this lecture you should be
able to:
• Recognize the need for a new theory that deals
with matter in reduced scales;
• Enunciate the postulates of Quantum Mechanics
History
By the end of the 19th century...
Matter and radiation were described by Newtonian
Mechanics and Maxwell’s equations, respectively
Interaction between matter and radiation was
explained by the Lorentz force
Particle and wave properties were mutually exclusive
History
Blackbody radiation
Photoelectric effect
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Compton effect
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In spect
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Louis de Broglie proposed that not only
waves behave like particles but that all matter
should also have a wave-like behaviour
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History
Wave aspects of particles
Matter waves and the de Broglie hypothesis
Davisson-Germer experiment
• Consider the following experiment: “classical” particles are allowed through
a narrow gap. The blue curve displays how they are spatially distributed
... and now through two separate gaps. The distribution is just a simple
addition of the two individual distributions
• The double slit experiment with electrons displays interference patterns
• Now suppose that we try to determine which slit the electron has moved
through. In this case, the interference pattern disappears.
• The double slit experiment with electrons displays interference patterns
• Now suppose that we try to determine which slit the electron has moved
through. In this case, the interference pattern disappears.
Complementarity Principle:
Particle and wave properties are not mutually
exclusive, but complementary
An experiment designed to isolate the particle
features of a quantum system gives no information
about its wave features and vice-versa.
In summary:
Corpuscular aspects of radiation and wave aspects of particles
Blackbody radiation
Photoelectric effect
Compton effect
Matter waves and the de Broglie hypothesis
Davisson-Germer experiment
Wave-particle duality and complementarity
principle
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Emission spectrum of the Hydrogen atom not
explained by classical Physics
• Explained by Bohr’s atomic model, who introduced
the concept of stationary orbits of quantized angular
momentum
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