Dirac Lecture 1 (of 4) - Quantum Mechanics --- The Bohr Orbit 00:00 Success of Rutherford and Bohr orbit theory 00:38 Rutherford model, positive nucleus with electrons around it 00:50 Bohr found laws regarding motion of electrons - normal Newtonian classical laws but ignore radiation emission 01:50 Resolves why do electrons not fall into nucleus and emit radiation 02:20 Bohr added quantum conditions related to Planck constant 02:30 Electron jumps from orbit to orbit and emits quantum of radiation 03:05 Frequency related to energy through Planck constant 03:30 Successful in describing single electron systems, hydrogen and alkali elements --- Extended by Hamilton 04:15 Bohr orbit theory revelation and acceptance 04:50 Sommerfeld added Hamiltonian variables of coordinates and momentum 05:33 Lagrange formulation of any function of position and velocities 05:50 Hamilton, 100 yrs earlier, replacing coordinates with momentum led to symmetry 07:00 Studied Hamiltonians by reading Whitaker and invariance of transformations --- Problem with interaction of orbitals 07:47 Difficulties occur on interaction of orbits 08:00 Helium spectrum appears as 2 different spectra with rare interaction 08:30 Two kinds of helium - para and ortho --- Heisenberg matrix mechanics 09:00 Heisenberg in 1925 introduces matrix mechanics 11:00 Understands importance of Heisenberg method 11:30 Bohr orbits not physical, cannot observer electrons, observations always involve 2 states 12:20 Concentrate on observations and represent particles as matrix arrays 13:30 Heisenberg handles matrices mathematically - multiplication does not compute, ie. A*B <> B*A --- Matrix non-commutation 15:20 Dirac concentrates on non-commutation and adds to Newtonian mechanics 16:50 Describes discovery that non-commutation and Poisson bracket are same thing in 1925 20:20 Definition of Poisson bracket - p's and q's are Hamiltonian coordinates and momentum 22:20 Equation shows direct relationship and describes path from any classical system to new mechanics 23:08 Heisenberg (with Born) showed same thing through degrees of freedom 24:20 Equations of motion - hamiltonian q/p variables represent total energy 25:40 Schrodinger's quantum mechanics - equivalent to Heisenberg theory, only needed to add wave function --- Atomic State subject to wave equation 27:50 Matrices associated with 2 atomic states, wave function represents an atomic state 28:08 Wave funtion Psi = function of particle coordinates x1, x2, x3 and time 28:30 Subject to wave equation where some operators produce zero 29:00 de Broglie's free particle wave equation shows momentum and energy equations are relativistic 31:00 Schrodinger applied de Broglie's free particle in an electric field 31:32 Hydrogen energy level calculation is wrong due to lack of term for spin component 32:47 Non-relativistic approximation gave correct Hydrogen energy levels 34:25 Wave equation is the Klein-Gordon equation --- Quantum mechanics allows addition of spin 35:32 Schrodinger adds to Heisenberg theory to give single state 35:48 Heisenberg matrices correspond to linear operators applied to wave functions 36:05 Commutation relation between momentum and coordinate variables are same in 2 theories 37:50 Quantum mechanics more general then classical mechanics 38:35 Quantum mechanics can use any functions to give equations of motion for any hamiltonian variables 39:30 Ie., 3 componenets of spin s1, s2, s3 that satisfy same conditions as orbital angular momentum 41:06 Spin variables not expressable as q's and p's at all times --- Mathmatical groups classify particles 42:10 Use groups, SU2 or SU3 to describe new particles being discovered 43:22 Used to study system with many particles - ie. lots of electrons 44:00 Symmetrical vs anti-symmetrical wave function permutation operators expands quantum mechanics 45:18 Explained the spectrum of ortho and para helium 45:47 Operators can be used for absorption and emission of particles, number of particles is not conserved 46:20 Led to Fields in Quantum Mechanics, allows for transformation of general dynamical variable 46:54 Average value of dynamic variable and their powers allows you to calculate probability of value 48:10 Formula for probability of particular value is square of modulus of wave function 49:00 P's and Q's do not commute so one cannot be calculated from the other --- Not the end, more will come 50:15 Probability is best we can do with existing quantum mechanic formulas - does god play dice? 51:05 Bohr correct on existing quantum mechanics, but fundamental difficulties exist 52:00 People forget problem of interacting Bohr orbitals, but are too complacent in accepting current QM 52:35 Final answer will involve large basic change in ways of thinking 52:50 Who knows what will happen to determinism, we cannot go back to classical physics

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