CC105Mid2Notes - Quantum 1 07/10/2008 13:51:00 Quantum...

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Unformatted text preview: Quantum 1 07/10/2008 13:51:00 Quantum Theory ( also called Quantum Mechanics) Describes the behavior of matter and light on small scales Quantum Theory II 07/10/2008 13:51:00 Schrodingers Wave Equation- h 2 2 m 2 Y( x ) x 2 + V ( x )Y( x ) = E Y( x ) h = h 2p shows the probability of finding a particle in a certain area. Particle in a Box o For an electron in a box that is 10- 9 m in size,: o E = h 2 8 mL 2 = 6 10- 20 J = 0.4 eV Hydrogen Atom o Solution of Schrdingers equatioon for the hydrogen atoms yields quantized electron energy levels n. The numner of wave function solutions increases with the quantum number n. o As is the case for the older Bohr model, the energy of each level is: E = 13.6 eV n 2 After passing through the slit, the wave has acquired a range of momentum in x-direction p o Its not possible to simultaneously measure the position and momentum of a particle with perfect accuracy: o There are other pairs of complementary variables, for example: o Et h/2 Cannot instantaneously measure energy with perfect accuracy. Quantum Theory and Reality Copenhagen Interpretation of Quantum Mechanics: o The wavefunction of an object evolves until a measurement is made. At that point the wavefuction collapses to give the measured value of wahtever variable is being examined (e.g. momentum, energy, position) In this point of view its only possible to ask about what actually is measured, NOT how the particle came to bein the state. o The classical Physics we can talk about the trajectory of a aprticle emitted at a point A and measured at point B: Ex/ A----------B p=mv o In quantum mechanics we can only talk about the measurement of the particle at point B NOT about the trajectory from A to B. In fact, to calculate the wave function of the particle at point B, we must use a SUPERPOSITION Ex/ A ? B Hidden Variables. o Are there variables that we arent aware of concerning probablility of a quantum system. Is there a physical characterisitc (hidden variable) that we dont know yet that effects a system? o 1964- John Bell proved: Experimentally testable statistical inequalities which have ruled out a broud class of hidden cariables-though limited possibilities remain. Alterntate Interpretations of Quantum Mechanics --New forms of Copenhaggen Interpretation: One key issue is how to incorporate the observer within a quantum mechanical framework since the original Copenhagen Interpretation treated the measurement/observer in a special manner- it causes the collapse of the wave function....
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CC105Mid2Notes - Quantum 1 07/10/2008 13:51:00 Quantum...

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