Transcript Year 2 - Quantum Mechanics

Year 2 - Quantum Mechanics
Lecture 2
Paul Dauncey
13/10/2008
Paul Dauncey - Quantum Mechanics
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Overview of lectures
• Lecture 1: Introduction
• Lectures 2-7: The Schrodinger equation and some
solutions in 1D
• Lectures 8-20: Measurements and the formal
basis of quantum mechanics
• Lectures 21-26: Quantum mechanics in 3D
• Lectures 27-29: Spin
• Lecture 30: Interpretations of quantum
mechanics
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Previously on QM
• Saw Hamilton’s method for classical
mechanics
– Two eqns: dx/dt = p/m = f(p)
-dp/dt = dV/dx = g(x)
• Saw the de Broglie relations
– Particle↔waves: E = ħω, p= ħk
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What we will do today
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Use the de Broglie relations as a guide
Consider the Schrodinger equation
Show it has to have a complex field y(x,t)
Think about what the complex field means
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5th Solvay Conference, Brussels, Oct 1927
Schrödinger
de Broglie
Debye
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How science works...
“Once at the end of a colloquium I heard Debye saying something
like “Schrödinger, you are not working right now on very
important problems ... why don't you tell us some time about
that thesis of de Broglie which seems to have attracted some
attention?” So, in one of the next colloquia, Schrödinger gave a
beautifully clear account of how de Broglie associated a wave
with a particle, and how he could obtain the quantisation rules ...
by demanding that an integer number of waves should be fitted
along a stationary orbit. When he had finished, Debye casually
remarked that he thought that this way of talking was rather
childish .... To deal properly with waves, one had to have a wave
equation.”
Felix Bloch, Address to the American Physical Society (1976) Quoted in 'An Introduction to Quantum Physics', A.P. French and
E.F. Taylor, Nelson, 1979 (page 104).
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Interpretation of y
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