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*> 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*

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