* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Torres: Copenhagen Quantum Mechanics
Aharonov–Bohm effect wikipedia , lookup
Elementary particle wikipedia , lookup
Quantum dot wikipedia , lookup
Atomic orbital wikipedia , lookup
Delayed choice quantum eraser wikipedia , lookup
Scalar field theory wikipedia , lookup
Quantum field theory wikipedia , lookup
Density matrix wikipedia , lookup
Quantum fiction wikipedia , lookup
Identical particles wikipedia , lookup
Wheeler's delayed choice experiment wikipedia , lookup
Renormalization wikipedia , lookup
Quantum computing wikipedia , lookup
Schrödinger equation wikipedia , lookup
Orchestrated objective reduction wikipedia , lookup
Measurement in quantum mechanics wikipedia , lookup
Renormalization group wikipedia , lookup
Erwin Schrödinger wikipedia , lookup
Bell's theorem wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Quantum entanglement wikipedia , lookup
Quantum machine learning wikipedia , lookup
Quantum group wikipedia , lookup
Coherent states wikipedia , lookup
Quantum key distribution wikipedia , lookup
Wave function wikipedia , lookup
Many-worlds interpretation wikipedia , lookup
Ensemble interpretation wikipedia , lookup
Atomic theory wikipedia , lookup
History of quantum field theory wikipedia , lookup
Quantum teleportation wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Path integral formulation wikipedia , lookup
Hydrogen atom wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Double-slit experiment wikipedia , lookup
Probability amplitude wikipedia , lookup
Canonical quantization wikipedia , lookup
Quantum state wikipedia , lookup
Particle in a box wikipedia , lookup
EPR paradox wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Wave–particle duality wikipedia , lookup
Matter wave wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Heisenberg: Mathematics is sense! That’s what sense is! Bohr: But in the end, in the end, remember, we have to be able to explain it all to Margrethe! COPENHAGEN QUANTUM MECHANICS PEOPLE REVIEW Max Plank 1858-1947 Albert Einstein 1879-1955 Neils Bohr 1885-1962 Werner Heisenberg 1901-1976 Erwin Schrödinger 1887-1961 WHAT IS QUANTUM, AND IS IT AS BAD AS THE JAMES BOND FILM? A Quantum is defined as the smallest bit of anything Quantum Mechanics= Mechanics of the very small Not even science can explain how terrible Quantum of Solace was SOME SIMPLE QUANTUM MECHANICAL SYSTEMS Special Relativity- E2=p2c2+m2c4 Planck- E=hf For a massless particle, E=pc ʎf=c Gives us: ʎ=h/p Early 20s, deBroglie proposed that any mass would correspond to a wavelength 1929, deBroglie Nobel Prize 1926, Erwin Schrödinger creates equation that predicts this wave deBroglie predicted Ψ(x,y,z,t) Could be used for any particle Fundamental equation of ALL quantum mechanics Güten tag. ich heiße Erwin Schrödinger A CLOSER LOOK iħ=( )(reduced Planck’s constant) d/dt = Time derivative Ψ(r,t) = Wave function = Laplacian function V(r,t)= Potential Energy CLASSICAL VERSUS QUANTUM http://tinyurl.com/c8t3e94 Classical: A Quantum: B-F Probability to find the particle in any one spot is equal classically and particle can have any value Probability to find the particle in any one spot is not equal at the quantum level Confines wavelength to ʎn=2l/n INTERPRETATIONS OF THE WAVE FUNCTION Interpretation 1: “Ok, wow, that’s kinda gross” Interpretation 2: Calculus? Yes. Interpretation 3: “But Chris, what does that imply?” TUNNELING Objects move through barriers Probability to find the wavefunction on the opposite side of the barrier is not zero HYDROGEN ATOM Probable positions of electrons are not exactly set Based on energy levels DISTINCTION BETWEEN LARGE AND SMALL None of this could happen on the visible scale “it becomes important to remember that science is concerned only with observable things and that we can observe an object only by letting it interact with some outside influence” -Dirac This interaction, observation, causes a disturbance on the quantum scale Traditional causality only applies to undisturbed systems NO CATS WERE HARMED IN THE MAKING OF THIS PHYSICS THE UNCERTAINTY PRINCIPLE? Werner Heisenberg 1925-1926 Values of position and momentum cannot both be precisely known. Measuring one with greater precision lowers the accuracy of the other BOHR EINSTEIN DEBATES God does not play dice. Stop telling God what to do. EINSTEIN’S BOX- 1930 Box of mass “m” with a clock that controls a shutter Box releases a photon in some arbitrary time t creating a change in mass E=mc2 gives precise energy THE DOUBLE SLIT EXPERIMENT http://tinyurl.com/yzttx3 Wave particle duality Electrons interfere with themselves as waves but strike the detector as particles