The Stern-Gerlach (SG) apparatus splits a wave-packet according to the projection of the spin of the particle on the direction of the magnetic field.
However, in some experiments, we need to reverse this splitting, i.e. to merge back the beams into a wave-packet identical with the initial one. The 1st candidate for such an operation would be a SG apparatus with opposite magnetic field.
But, it is known that this scheme doesn't work well, the initial wave-packet is not restored properly.
Does somebody know a better scheme?
My problem is to split and restore the wave-packet of a spin 1 particle. I would be glad if somebody could suggest another property than spin, that has three discrete eigenvalues, 0, 1, and -1, and allows precise splitting and restoring of the wave-packet.
Hi Sofia,
It's probably not much help, but the first thought triggered by your question is whether you could somehow make use of parity, with eigenvalues of +1 and -1, but I don't see how to get the 0 in too...
Paul
Thanks Paul for trying to help, but the 0 is indeed essential.
Kindest regards from me!
Dear Sofia; In a corpuscular approach let me say: As soon as there are two objects in interaction let say one electron with one proton they must be in motion between them otherwise they will belong to just one object. In addition there are necessary two motions between them: one of translation the other of rotation.
For the rotation is it possible to consider two different rotation? Generally in the wave approach, considering the orbit, people suppose two kind of rotation call spin. In a corpuscular approach, with respect of the orbit, it is an error because the orbit is an immaterial line. I discuss the Stern and Gerlach experiment in “Quantum State and Periodicity” on my RG site.
I will be glad if you find questioning this remark, Yours Xavier
Dear Xavier,
Many thanks for kindly trying to help me. But, what I need is not a discussion of the Stern-Gerlach experiment. I need some substitute of it, which would be more precise. I quote here again my problem:
==> "However, in some experiments, we need to reverse this splitting (done by the SG apparatus), i.e. to merge back the beams into a wave-packet identical with the initial one. The 1st candidate for such an operation would be a SG apparatus with opposite magnetic field. But, it is known that this scheme doesn't work well, the initial wave-packet is not restored properly."
Since for testing the observable spin-projection I don't know a better apparatus than the SG, I ask if somebody can suggest another discrete observable with 3 eigenvalues, and an appropriate apparatus for testing them.
With best regards,
Sofia
It is difficult to answer without knowing precisely the initial "state" of your experiment and what you expect. In the Stern Gerlach experiment you will have two main effects 1) the lateral separation of the magnetic sub levels due to the gradient of the magnetic field 2) a longitudinal separation due to the magnetic field itself, which is used as a quantization axis that constrained the precession. Note that if you act with zero field configuration you will have multiple interferences situations that are quite impossible to control without much care. Disregarding of the longitudinal lag between the wave packets for different sub levels allows nevertheless to recombine the different part only if they arrive with the appropriate directions (related to the quantization axis) in the SG device.
If you need more informations, I can explain that to you more lengthly.
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