Year 2 - Quantum MechanicsLecture 2

Paul Dauncey

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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

• Use the de Broglie relations as a guide• Consider the Schrodinger equation• Show it has to have a complex field(x,t)• Think about what the complex field means

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5th Solvay Conference, Brussels, Oct 1927

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Debye

Schrödingerde Broglie

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

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