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!

 Max Plank  Albert Einstein  Neils Bohr  Werner Heisenberg  Erwin Schrödinger

 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

 Special Relativity- E 2 =p 2 c 2 +m 2 c 4  Planck- E=hf  For a massless particle, E=pc  ʎ f=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

 iħ=( )(reduced Planck’s constant)  d/dt = Time derivative  Ψ(r,t) = Wave function  = Laplacian function  V(r,t)= Potential Energy

  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 ʎ n =2l/n

 Interpretation 1: “Ok, wow, that’s kinda gross”  Interpretation 2: Calculus? Yes.  Interpretation 3: “But Chris, what does that imply?”

 Objects move through barriers  Probability to find the wavefunction on the opposite side of the barrier is not zero

 Probable positions of electrons are not exactly set  Based on energy levels

 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

 Werner Heisenberg  Values of position and momentum cannot both be precisely known.  Measuring one with greater precision lowers the accuracy of the other

God does not play dice. Stop telling God what to do.

 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=mc 2 gives precise energy

  Wave particle duality  Electrons interfere with themselves as waves but strike the detector as particles