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Transcript
The Physical Meaning of the Wave Function 1 Wave Function for Light in Classic Mechanics Superposition creates regions of constructive and destructive diffraction according to the relative incidence of the waves. The light intensity is distributed by the square of the wave envelope: (r ) 2 2 intensity = energy Volume unit The Particle-like Nature of the Measuring Process The beam of electrons is distributed according to its wavelike nature. Does each electron behave like a wave, hitting the screen in several places simultaneously? 3 The Particle-like Nature of the Measuring Process During the measurment the electron behaves like a particle: it can be in one place only. The wave function determines the distribution (probability density) for finding the electron in a specific position 4 Base Transitions The information implicit in the wave function enables to transform between various presentations of the particle properties. The position picture: (x) The momentum picture: g(k) Fourier Transform The probability for finding a particle with a specific momentum 5 g ( k ) k 2 Wave Function for Light in Quantum Mechanics For a large number of n particles 6 Quantum Mechanics Postulates for a 1-dimension Free Particle 1. (The tools of the game) The system status can be described by a wavepacket (the board of the game) pertaining to the space of continuous functions on the x axis: 2. (The rules of the game) For each component in the wavepacket the following is true: 3. (The interface) the measuring action has the following probability of finding the particle in a single length element dx: 7 Probability Density The odds of finding a particle between x and x+dx: The odds of finding a particle between x1 and x2: The odds of finding a particle in the whole space (normalization) 8
