1. Year 2 - Quantum Mechanics Lecture 2 Paul Dauncey 13/10/20081Paul Dauncey - Quantum Mechanics

2. 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 13/10/20082Paul Dauncey - Quantum Mechanics

3. 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 13/10/20083Paul Dauncey - Quantum Mechanics

4. 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 13/10/20084Paul Dauncey - Quantum Mechanics

5. 5 th Solvay Conference, Brussels, Oct 1927 13/10/20085Paul Dauncey - Quantum Mechanics Debye Schrödinger de Broglie

6. 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). 13/10/20086Paul Dauncey - Quantum Mechanics

7. Interpretation of  13/10/20087Paul Dauncey - Quantum Mechanics