A wavepacket is a superposition of many states. So how can it describe ONE particle?by aaronsky12 Tags: group velocity, quantum number, state, wavepacket 

#1
Nov412, 03:53 PM

P: 3

I was taught that a particle is assigned to a unique quantum state. As a specific example, two bound electrons can't have the same quantum numbers in an atom. And likewise one and only bound electron is assigned to one quantum state in an atom. Yet, I am reading several solid state books and they are saying that an electron moving in a conductive material (crystal lattice) can be described by a localized wavepacket with a group velocity and central energy... That makes sense intuitively... but wavepackets are themeselves superpositions of sinusoidal traveling wave solutions to shrodinger's equation (each with a wavevector k)... This makes it sound like one particle is assigned several wavefunctions (each with their own quantum numbers)... How can this be true???




#2
Nov412, 11:40 PM

Sci Advisor
PF Gold
P: 2,046

Mate its the principle of superposition at work:
http://en.wikipedia.org/wiki/Quantum_superposition Thanks Bill 



#3
Nov512, 01:05 AM

P: 977

Have not you heard that an arbitrary wave can be expressed by superposition of many plane waves(provided complete sets) and also schrodinger eqn is linear so it should hold.




#4
Nov512, 05:05 PM

P: 3

A wavepacket is a superposition of many states. So how can it describe ONE particle?
Thanks bhobba and andrien!! OK, here is a related follow up question... First let me quote the wiki pages for the superposition principle and Pauli Exclusion principle state:
"[Quantum superposition] holds that a physical system—such as an electron—exists partly in all its particular, theoretically possible states (or, configuration of its properties) simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations (as described in interpretation of quantum mechanics)." "The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with halfinteger spin) may occupy the same quantum state simultaneously." My question is: Can two electrons "share" states and not violate the exclusion principle. It makes sense that one electron can exist in state A and another electron in B. But can one electron exist partially in state A and B, while the other also exists in partially state A and B at the same time? 



#5
Nov612, 06:41 AM

P: 977





#6
Nov612, 10:11 AM

Sci Advisor
Thanks
P: 3,853

So if you have electron A in the state z,+> and electron B in the state z,>, you can say that they are both partially in states x,+> and x,>. 



#7
Nov612, 11:52 AM

P: 724

Electrons are fermions and cannot occupy the same quantum state. This is taken care of by the PEP. Photons(bosons) on the other hand can, hence light is not solid. 



#8
Nov712, 09:57 AM

Sci Advisor
Thanks
P: 3,853





#9
Nov812, 04:02 PM

Mentor
P: 10,798





#10
Nov912, 07:26 AM

P: 977




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