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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?
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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:
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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)
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