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States and wave functions (Read 2410 times)
Gerrit-Jan Linker
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States and wave functions
19.01.08 at 12:27:56
 
States and wave functions
 
The state of a system is fully described by a function Ψ(r1,r2,...,t) in which ri = spatial coordinates of particle i and t = time.
 
Ψ is called the wave function of the system and the time independent form of it is Ψ(r1,r2,...)
 
The wavefunction of a system can be specified by a set of quantum numbers (a,b,c,...) so the state of a system can be written as Ψa,b,c,...
 
See also:
Superposition principle  
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« Last Edit: 04.02.08 at 21:13:19 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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Gerrit-Jan Linker
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Re: States and wave functions
Reply #1 - 28.07.08 at 11:05:55
 
Quote:
The wave function Ψ is a function of the coordinates, or position vectors, {r} of the particles of intrest, possibly of some intrinsic variable of the particles, such as spin, and of time, t, and contains the information on the motion of the particles through space as a function of time:
Ψ = Ψ( {x}; r )
in which {x} collects the position vectors and intrinsic variables of the particles.

Once the wave function is known all properties of the system can be computes as so called expectation values, which are integrals of the wave fnction, normalized to unity, over an operator O associated with the proerty of interest.

 
Source: Thesis Alex de Vries, Groningen, 1995
 
In quantum mechanics a system is described by a wave function. Observable properties of a system correspond to an operator that works on the function.
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Gerrit-Jan Linker
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Interpretation wavefunction
Reply #2 - 07.02.11 at 19:13:54
 
Interpretation wavefunction
 
 
Ψ*( {x,t} ) Ψ( {x,t} ) dx1dx2...dxN = |Ψ( {x,t} )|2 dx1dx2...dxN
 
this is the chance to encounter particle 1 between x1 and (x1 and dx1), particle 2 between x2 and (x2 and dx2), .... particle N between xN and (xN and dxN)
 
All particles need to be somewhere so,
∫ |Ψ( {x,t} )|2 dx1dx2...dxN = 1
 
Copenhagen interpretation
Pioneered by the Danish physicist Niels Bohr
THe wavefunction is a computational tool. It gives correct results when used to calculate the probability of particles having various properties. There is no deeper explanation of what a wavefunction is.
 
Others, such as Erwin Schrodinger, considered the wavefunction , at least initially, to be a real physical object.
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« Last Edit: 18.11.11 at 22:53:38 by Gerrit-Jan Linker »  

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