28D matter waves, uncertainty

28D matter waves, uncertainty - 5/22/2011 Outline Physics...

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5/22/2011 1 Physics 1C Lecture 28D "I ask you to look both ways. For the road to a knowledge of the stars leads through the atom; and important knowledge of the atom has been reached through the stars." --Sir Arthur Eddington Outline An Interpretation of QM Particle in a box Atomic physics Emission spectra Absorption spectra An Interpretation of QM Probability V N I V  2 IE Particle interpretation: Wave interpretation: the intensity is proportional to the square of the electric field amplitude: 2 Probability V E Combine the two points of view: For EM radiation, the probability of finding a particle associated with this radiation is proportional to the square of the amplitude of the associated EM wave. The particle is the photon in this case. The amplitude of the wave is called the probability amplitude or the wave function . The symbol is y . An Interpretation of QM The probabilistic interpretation of the wave function was suggested by Max Born in 1928. Erwin Schrödinger proposed a wave equation which describes the manner in which the wave function changes in space and evolves with time. This equation is a key element in the theory of quantum mechanics. If represents a single particle, | | 2 is the relative probability per unit volume that the particle will be found at any given point in the volume. | | 2 is called the probability density. Particle in a Box Let’s consider a particle confined to a one- dimensional region in space. Following the quantum mechanics approach, we need to find an appropriate wave function to describe the motion of the particle. Because of the walls, the probability of finding the particle outside the box is zero. This means that ( x )=0 for x 0 and for x L . When the particle is inside the box, the potential energy of the system is constant. Particle in a Box 2 ( ) sin x xA  =   We can define the potential energy to be infinitely large outside the box.
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28D matter waves, uncertainty - 5/22/2011 Outline Physics...

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