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Particle Superposition 
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#1
Mar1709, 03:31 PM

P: 125

Hello, 've been progressing through my selfstudying of the Schrodinger Equation in both its timedependent and independent forms, and I have come across an unknown term.
Super Position ( in my book it's translated in greek literally superposition = υπέρθεση) My guess so far is that a superposition is when a particle is described by two wavefunctions, which happen to be two eigenfunctions [itex]\psi_n[/itex]with the same (perhaps with different, {not sure there} ) eigenvalues En. Am I correct? If not, please enlighten me :) 


#2
Mar1709, 03:46 PM

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P: 4,738

well it does not have to be a particle either! :)
But consider deuterium, a bound proton  neutron state. It's state function is a linear combination of two terms: http://en.wikipedia.org/wiki/Deuteri...f_the_deuteron 


#3
Mar1709, 04:21 PM

P: 125

I think "Linear Combination of Wavefunctions" was the term I was looking for, eh?



#4
Mar1709, 04:35 PM

P: 192

Particle Superposition
[tex]\phi_n = A sin(\frac{n \pi x}{L}) [/tex] Where A is a normalization factor. Just because a particle is in this box, does not mean that it is one of the states, those are only the states with definite well defined energy. A particle could be in a super position of energy eigenstates: [tex]\psi= B sin(\frac{\pi x}{L}) + C sin(\frac{2 \pi x}{L})[/tex] where a condition on B and C is to normalize the wavefunction, as usual. Notice that the two states which are involved are the n = 1 state (the B term) and the n = 2 state (the C term). Now when we measure the energy of a particle in this state we do not know whether you will get n = 1 or n = 2 but we can calculuate the probabiity of either! 


#5
Mar1809, 03:41 AM

P: 125

Thank you! Really nice explanation there!



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