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

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

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

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

15:20   Dirac concentrates on noncommutation and adds to Newtonian mechanics

16:50   Describes discovery that noncommutation 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

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   Nonrelativistic approximation gave correct Hydrogen energy levels

34:25   Wave equation is the KleinGordon equation

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

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 antisymmetrical 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

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
