Animated Physics - Paul Dirac Live

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Paul Dirac Live!

Dirac himself discussing the history of quantum mechanics and source of his discovery of the "Dirac Equation". He shows how the Poisson Bracket matches his commutators and expands on the Klien-Gordon equation for spin.

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Dirac Lecture 1 (of 4) - Quantum Mechanics

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

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