> scerir wrote:
> A single particle is prepared in a (weird) superposition.
> The superposition consists in being in three boxes.
> The initial state is |psi_1>
> |psi_1> = 3 ^ (-1/2) ( |A> + |B> + |C> )
> and the final state is |psi_2>
> |psi_2> = 3 ^ (-1/2) ( |A> + |B> - |C> )
> where A, B and C are the three boxes.
> If you search, in the intermediate time, in the box A
> you'll find the particle. Otherwise the state would be
> |psi_huh> = 2 ^ (-1/2) ( |B> + |C> ) which is forbidden
> being orthogonal to the final state.
> If you search, in intermediate time, in the box B
> you'll find the particle. Otherwise the state would be
> |psi_hoh> = 2 ^ (-1/2) ( |A> + |C> ) which is forbidden
> being orthogonal to the final state.
> Then the single particle is in the box A (searching in A)
> and in the box B (searching in B).
> What about searching in A *and* B? I don't know.
> And it's too late now. And QM is a nasty trick.
A1. Spot the humour....
|psi_h_uh_oh>
or perhaps
|psi_huh>, |psi_hoh> and |psi_off_to_work_we_go>
do I get a prize?
A2.
I survive on 25 year old engineering maths and 2nd year (3rd year?) QM
course, so bear with me on this while you folk update my education. I need a
little help.....
> A single particle is prepared in a (weird) superposition.
We are going to transform the properties (wave function?) of a particle.
> The superposition consists in being in three boxes.
Interpreted to mean: When the superposition transformation is complete the
probability of spatial position in one of 3 defined regions of space is
controlled to a defined extent.
> The initial state is |psi_1>
> |psi_1> = 3 ^ (-1/2) ( |A> + |B> + |C> )
psi_1 is a vector. A, B, C are orthogonal vector representations of the
spatial distribution of the state, normalised (1 over root 3).
> and the final state is |psi_2>
when the quantum wierdness has been applied the new state is
> |psi_2> = 3 ^ (-1/2) ( |A> + |B> - |C> )
.ie. a vector subtraction the component in the C reverses the C component
and leaves A and B alone.
> where A, B and C are the three boxes.
> If you search, in the intermediate time, in the box A
meaning you make a measurement in region A and collapse the wave function to
give an accurate position *prior to the transformation*
> you'll find the particle.
will you? In multiple measurements you'll get the particle a proportion of
the time but not all ...at least that's what I thought the a wave function
of position meant. In a single measurement all you have is a proability of
'find'.
> Otherwise the state would be
> |psi_huh> = 2 ^ (-1/2) ( |B> + |C> ) which is forbidden
> being orthogonal to the final state.
Having done the measurement, isn't the process of carrying out the
transformation meaningless?
The measurement forces all 'position' into box A. We then do a
transformation involving C. How can the final state end up as the stated
|psi_2 without altering the transformation?
> If you search, in intermediate time, in the box B
> you'll find the particle. Otherwise the state would be
> |psi_hoh> = 2 ^ (-1/2) ( |A> + |C> ) which is forbidden
> being orthogonal to the final state.
> Then the single particle is in the box A (searching in A)
> and in the box B (searching in B).
You have a probability of a 'find' increase by the contribution of A and B
totalled up?
> What about searching in A *and* B? I don't know.
I question the nature of the 'measurement'. The question assumes that the
measurement is of a type designed to resolve the quantity 'position' in
region A. If the measurement were redined/re-engineered to resolve position
in both regions A or B, then you'll get a combined result. If you make two
simultaneous A-type measurements then you'll 'find' it either in A or B but
not both in proportion to the A and B vector contributions. Yes?
> And it's too late now. And QM is a nasty trick.
Damn right.
Maybe I'm just totally off the track. Maybe when you say 'being in 3 boxes'
you mean classified in one of 3 ways (eg spin, velocity, position). I
struggle with the jargon. Thanks for making me think.
cheers
:)
Col
*I suppose doing QM late at night and expecting sense is pretty funny*
This archive was generated by hypermail 2b30 : Sat May 11 2002 - 17:44:13 MDT