# Copenhagen Quantum Mechanics - University of Notre Dame

Heisenberg: Mathematics is sense! Thats 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 Schrdinger 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 f=c Gives us: =h/p Early 20s, deBroglie proposed that any mass would correspond to a wavelength 1929, deBroglie Nobel Prize 1926, Erwin Schrdinger Gten

creates equation that tag. predicts this wave deBroglie ich heie Erwin predicted (x,y,z,t)x,y,z,t) Schrding Could be used for any er particle Fundamental equation of ALL quantum mechanics A CLOSER LOOK

i=(x,y,z,t) )(x,y,z,t)reduced Plancks constant) d/dt = Time derivative (x,y,z,t)r,t) = Wave function = Laplacian function V(x,y,z,t)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 n=2l/n

INTERPRETATIONS OF THE WAVE FUNCTION Interpretation 1: Ok, wow, thats 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. EINSTEINS 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

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