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The Physical Meaning of The Physical Meaning of the Wave Functionthe Wave Function

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Superposition creates regions of constructive Superposition creates regions of constructive and destructive diffraction according to the and destructive diffraction according to the relative incidence of the waves. The light relative incidence of the waves. The light intensity is distributed by the square of the intensity is distributed by the square of the wave envelope:wave envelope:

Wave Function for Light in Classic MechanicsWave Function for Light in Classic Mechanics

2)(r intensity =

energy

Volume unit

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The beam of electrons is distributed according The beam of electrons is distributed according to its wavelike nature. to its wavelike nature. Does each electron behave like a wave, hitting Does each electron behave like a wave, hitting the screen in several places simultaneously?the screen in several places simultaneously?

The Particle-like Nature of the Measuring ProcessThe Particle-like Nature of the Measuring Process

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During the measurment the electron behaves like a During the measurment the electron behaves like a particle: it can be in one place only. The wave function particle: it can be in one place only. The wave function determines the distribution (probability density) for determines the distribution (probability density) for finding the electron in a specific positionfinding the electron in a specific position

The Particle-like Nature of the Measuring ProcessThe Particle-like Nature of the Measuring Process

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The information implicit in the wave function enables to The information implicit in the wave function enables to transform between various presentations of the particle transform between various presentations of the particle properties.properties.

Base TransitionsBase Transitions

FourierFourier

TransformTransform

FourierFourier

TransformTransform

g(k)(x) The momentum picture:The momentum picture:The position picture:The position picture:

The probability for finding a particle with a The probability for finding a particle with a specific momentumspecific momentum k)k(g

2 k)k(g2

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For a large number of n particlesFor a large number of n particles

Wave Function for Light in Quantum MechanicsWave Function for Light in Quantum Mechanics

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Quantum Mechanics Postulates for a 1-dimension Quantum Mechanics Postulates for a 1-dimension Free ParticleFree Particle

1.1. (The tools of the game)(The tools of the game) The system status can be described by a The system status can be described by a wavepacket wavepacket (the board of the game)(the board of the game) pertaining to the space of pertaining to the space of continuous functions on the x axis:continuous functions on the x axis:

2.2. (The rules of the game)(The rules of the game) For each component in the wavepacket the For each component in the wavepacket the following is true:following is true:

3.3. (The interface) (The interface) the measuring action has the following probability of the measuring action has the following probability of finding the particle in a finding the particle in a singlesingle length element dx: length element dx:

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Probability DensityProbability Density

The odds of finding a particle between x and x+dx:The odds of finding a particle between x and x+dx:

The odds of finding a particle between xThe odds of finding a particle between x11 and x and x22::

The odds of finding a particle in the whole space (normalization)The odds of finding a particle in the whole space (normalization)