The effect of the magnet in a Stern-Gerlach experiment

• Fredrik
In summary, the conversation discusses the splitting of a beam of silver atoms in an inhomogeneous magnetic field, and the resulting state of the atoms being described as |U>|↓>+|L>|↑>. The conversation also mentions the possibility of using the wavefunction to explain this phenomenon, and references a textbook that discusses the deBB perspective on this experiment. The conversation also includes a link to a demonstration of the experiment and mentions the need to use the Pauli equation to fully understand it.

Fredrik

Staff Emeritus
Gold Member
A beam of silver atoms (which are electrically neutral spin-1/2 particles) enters an inhomogeneous magnetic field, and is split in two.

The state of an atom that has passed the magnet is often described as |U>|↓>+|L>|↑>, where |U> and |L> are states that are localized to the upper and lower paths respectively, and |↓> and |↑> are the "spin down" and "spin up" states respectively. I have realized that I don't really understand how to justify this. Can we prove that each atom will end up in a |U>|↓>+|L>|↑> state?

Bump.

One idea that occurs to me is to take the wavefunction to be of the exp(-a(x-vt)2) form for x<0, and the potential to be 0 for x<0 and x>1, and $$=\vec\mu\cdot\vec B$$ when 0<x<1, but then I don't see how we can impose a boundary condition at x=1. Do we need one? Is this problem worked out in any of the standard textbooks?

The detail I'm the most interested in is why the wavefunction changes from having one peak to having two peaks, instead of just spreading out. Is this a result of some sort of decoherence in which the magnet serves as an "environment", or can it be derived from the Schrödinger equation alone?

Hi Fredrik,

If you search through the archives, you'll find a thread - not too long ago - where you said you were going to order Peter Holland's "Quantum Theory of Motion" textbook - which is about the deBB perspective of these things. Did it ever arrive, I wonder? Anyway, there's a whole bunch of stuff about the SG experiment in there - though if you haven't got the physical book the crucial pages on Google Books are blocked, sadly.

Hey, it's even a demonstration on the Wolfram site:

http://demonstrations.wolfram.com/TheCausalInterpretationOfTheSternGerlachExperiment/" [Broken]

Since the Schroedinger equation is about spinless particles, you do need to go the level of the Pauli equation or whatever, obviously.

Cheers,
Zenith

Last edited by a moderator:
Thank you. It's been on my bookshelf for a long time, but I haven't read it yet. Not even a single page I'm afraid. I'm so dumb that it's taking me a very long time to learn functional analysis and a few other things that I've been giving a higher priority. I'll check it out.

1. How does a magnet affect the particles in a Stern-Gerlach experiment?

The magnet in a Stern-Gerlach experiment exerts a force on the particles, causing them to be deflected in specific directions based on their magnetic properties.

2. Why is a magnet used in a Stern-Gerlach experiment?

A magnet is used in a Stern-Gerlach experiment to separate particles with different magnetic moments, allowing for the study of their properties and behavior.

3. What is the purpose of the Stern-Gerlach experiment?

The Stern-Gerlach experiment is used to study the quantum behavior of particles, specifically their magnetic properties and the effects of external forces.

4. Can the strength of the magnet affect the results of a Stern-Gerlach experiment?

Yes, the strength of the magnet can affect the deflection of particles in a Stern-Gerlach experiment. A stronger magnet will exert a greater force on the particles, resulting in larger deflections.

5. What happens to the particles after they are deflected in a Stern-Gerlach experiment?

The particles are separated into different paths based on their magnetic properties and continue on to be detected by a measuring device, allowing for further analysis and understanding of their behavior.

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