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{{Quantum mechanics|cTopic=Experiments}}   
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The '''Stern–Gerlach experiment''',<ref>{{cite journal
|last=Gerlach |first=W.
|last2=Stern |first2=O.
|title=Das magnetische Moment des Silberatoms
|journal=[[Zeitschrift für Physik]]
|volume=9 |pages=353–355
|year=1922
|doi=10.1007/BF01326984
|bibcode = 1922ZPhy....9..353G }}</ref> named after German physicists [[Otto Stern]] and [[Walther Gerlach]], is an important experiment in [[quantum mechanics]] on the [[deflection (physics)|deflection]] of [[Elementary particle|particle]]s. This experiment, performed in 1922,  is often used to illustrate basic principles of quantum mechanics. It can be used to demonstrate that electrons and atoms have intrinsically quantum properties, and how [[measurement in quantum mechanics]] affects the system being measured. 


==Basic theory and description==
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{{See also|Spin quantum number}}
[[File:Quantum spin and the Stern-Gerlach experiment.ogv|thumb|upright=1.5|Quantum spin versus classical magnet in the Stern–Gerlach experiment]]
[[File:Stern-Gerlach experiment.PNG|300px|thumb|Basic elements of the Stern–Gerlach experiment.]]


The Stern–Gerlach experiment involves sending a beam of particles through an [[Homogeneity and heterogeneity|inhomogeneous]] [[magnetic field]] and observing their deflection. The results show that particles possess an intrinsic [[angular momentum]] that is closely analogous to the angular momentum of a classically spinning object, but that takes only certain quantized values.  Another important result is that only one component of a particle's spin can be measured at one time, meaning that the measurement of the spin along the z-axis destroys information about a particle's spin along the x and y axis.
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The experiment is normally conducted using electrically neutral particles or atoms. This avoids the large deflection to the orbit of a charged particle moving through a magnetic field and allows spin-dependent effects to dominate. If the particle is treated as a classical spinning [[dipole]], it will [[Larmor precession|precess]] in a magnetic field because of the torque that the magnetic field exerts on the dipole (see [[Gyroscopic precession|torque-induced precession]]). If it moves through a homogeneous magnetic field, the forces exerted on opposite ends of the dipole cancel each other out and the trajectory of the particle is unaffected. However, if the magnetic field is inhomogeneous then the force on one end of the dipole will be slightly greater than the opposing force on the other end, so that there is a net force which deflects the particle's trajectory. If the particles were classical spinning objects, one would expect the distribution of their spin angular momentum vectors to be [[continuous random variable|random and continuous]]. Each particle would be deflected by a different amount, producing some density distribution on the detector screen. Instead, the particles passing through the Stern–Gerlach apparatus are deflected either up or down by a specific amount. This was a measurement of the quantum [[observable]] now known as [[spin operator|spin]], which demonstrated possible outcomes of a measurement where the observable has [[point spectrum]]. Although some discrete quantum phenomena, such as [[atomic spectra]], were observed much earlier, the Stern–Gerlach experiment allowed scientists to conduct measurements of deliberately [[quantum superposition|superposed]] quantum states for the first time in the history of science.
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By now it is known theoretically that [[angular momentum operator#Quantization|quantum angular momentum ''of any kind'' has a discrete spectrum]], which is sometimes imprecisely expressed as "angular momentum is [[Quantization (physics)|quantized]]".
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If the experiment is conducted using charged particles like electrons, there will be a Lorentz force that tends to bend the trajectory in a circle (see [[Cyclotron#Mathematics of the cyclotron|cyclotron motion]]). This force can be cancelled by an electric field of appropriate magnitude oriented transverse to the charged particle's path.
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[[File:Quantum projection of S onto z for spin half particles.PNG|100px|left|thumb|Spin values for fermions.]]
 
Electrons are [[spin-½|spin-{{frac|1|2}}]] particles. These have only two possible spin angular momentum values measured along any axis, +ħ/2 or −ħ/2, a sheerly quantum mechanical phenomenon. Because its value is always the same, it is regarded as an intrinsic property of electrons, and is sometimes known as "intrinsic angular momentum" (to distinguish it from orbital angular momentum, which can vary and depends on the presence of other particles).
 
For electrons there are two possible values for the spin angular momentum that is measured along an axis. The same is true for the [[proton]] and the [[neutron]], which are composite particles made up of three [[quarks]] each (which are themselves [[spin-½|spin-{{frac|1|2}}]] particles. However, the three quarks do not consist of a pair that cancel each other out and a third quark that gives the net {{frac|1|2}} spin to the composite particle, as previously believed before the [[Proton spin crisis]] was discovered. Hence the intrinsic spin of the nucleons is orbital rather than intrinsic). Other particles have a different number of possible spin values. [[Delta baryon]]s ({{SubatomicParticle|Delta++}}, {{SubatomicParticle|Delta+}}, {{SubatomicParticle|Delta0}}, {{SubatomicParticle|Delta-}}), for example, are spin +{{frac|3|2}} particles and have four possible spin momentum values. [[Vector mesons]], as well as [[W and Z bosons]] are spin-1 particles that have three possible spin angular momentum values.
 
To describe the experiment with spin +{{frac|1|2}} particles mathematically, it is easiest to use [[Paul Adrien Maurice Dirac|Dirac]]'s [[bra–ket notation]]. As the particles pass through the Stern–Gerlach device, they are being observed by the detector which resolves to either spin up or spin down. These are described by the angular momentum quantum number ''j'', which can take on one of the two possible allowed values, either +ħ/2 or −ħ/2. The act of observing (measuring) the momentum along the z axis corresponds to the operator ''J''<sub>z</sub>. In mathematical terms,
:<math>|\psi\rangle = c_1\left|\psi_{j = +\frac{\hbar}{2}}\right\rangle + c_2\left|\psi_{j = -\frac{\hbar}{2}}\right\rangle</math>.
 
The constants ''c''<sub>1</sub> and ''c''<sub>2</sub> are complex numbers. The squares of their [[absolute value]]s (|''c''<sub>1</sub>|<sup>2</sup> and |''c''<sub>2</sub>|<sup>2</sup>) determine the probabilities that in the state <math>|\psi\rangle</math> one of the two possible values of ''j'' is found. The constants must also be normalized in order that the probability of finding either one of the values be unity. However, this information is not sufficient to determine the values of ''c''<sub>1</sub> and ''c''<sub>2</sub>, because they may in fact be complex numbers. Therefore the measurement yields only the absolute values of the constants.
 
==Sequential experiments==
If we link multiple Stern–Gerlach apparatuses, we can clearly see that they do not act as simple selectors, but alter the states observed (as in [[photon polarization|light polarization]]), according to [[quantum mechanics|quantum mechanical]] law:
<ref>
{{cite book
|first=J.-J. |last=Sakurai
|title=Modern quantum mechanics
|publisher=[[Addison-Wesley]]
|year=1985
|isbn=0-201-53929-2
}}</ref>
[[File:Sg-seq.svg|left|640px]]
{{clr}}
 
==History==
[[File:SternGerlach2.jpg|thumb|A plaque at the Frankfurt institute commemorating the experiment]]
The Stern–Gerlach experiment was performed in [[Frankfurt]], [[Germany]] in 1922 by [[Otto Stern]] and [[Walther Gerlach]]. At the time, Stern was an assistant to [[Max Born]] at the [[Goethe University Frankfurt|University of Frankfurt]]'s [[Institute for Theoretical Physics (Frankfurt)|Institute for Theoretical Physics]], and Gerlach was an assistant at the same university's [[Institute for Experimental Physics (Frankfurt)|Institute for Experimental Physics]].
 
At the time of the experiment, the most prevalent model for describing the [[atom]] was the [[Bohr model]], which described [[electrons]] as going around the positively charged [[Atomic nucleus|nucleus]] only in certain discrete [[atomic orbital]]s or [[energy levels]]. Since the electron was [[Quantization (physics)|quantized]] to be only in certain positions in space, the separation into distinct orbits was referred to as [[Old quantum theory#Rotator|space quantization]]. The Stern–Gerlach experiment was meant to test the [[Old quantum theory|Bohr–Sommerfeld hypothesis]] that the direction of the angular momentum of a silver atom is quantized.<ref>
{{cite journal
|first=O. |last=Stern
|title=Ein Weg zur experimentellen Pruefung der Richtungsquantelung im Magnetfeld
|journal=[[Zeitschrift für Physik]]
|volume=7 |pages=249–253
|year=1921
|doi=10.1007/BF01332793
|bibcode = 1921ZPhy....7..249S }}</ref>
 
Note that the experiment was performed several years before [[George Eugene Uhlenbeck|Uhlenbeck]] and [[Samuel Abraham Goudsmit|Goudsmit]] formulated their hypothesis of the existence of the [[Spin (physics)|electron spin]]. Even though the result of the Stern−Gerlach experiment has later turned out to be in agreement with the predictions of quantum mechanics for a spin-{{frac|1|2}} particle, the experiment should be seen as a corroboration of the [[Old quantum theory|Bohr–Sommerfeld theory]].<ref>
{{cite journal
|last=Weinert |first=F.
|title=Wrong theory—right experiment: The significance of the Stern–Gerlach experiments
|journal=[[Studies in History and Philosophy of Modern Physics]]
|volume=26B |pages=75−86
|year=1995
|doi=10.1016/1355-2198(95)00002-B
}}</ref>
 
In 1927, T.E. Phipps and J.B. Taylor reproduced the effect using [[hydrogen]] atoms in their [[ground state]], thereby eliminating any doubts that may have been caused by the use of [[silver]] atoms.<ref>
{{cite journal
|last=Phipps |first=T.E.
|last2=Taylor |first2=J.B.
|title=The Magnetic Moment of the Hydrogen Atom
|journal=[[Physical Review]]
|volume=29 | issue=2 | pages=309–320
|year=1927
|bibcode=1927PhRv...29..309P
|doi=10.1103/PhysRev.29.309
}}</ref> (In 1926 the non-relativistic [[Schrödinger equation]] had incorrectly predicted the [[magnetic moment]] of hydrogen to be zero in its ground state. To correct this problem [[Wolfgang Pauli]] introduced "by hand", so to speak, the 3 [[Pauli matrices]] which now bear his name, but which were later shown by [[Paul Dirac]] in 1928 to be intrinsic in his [[Introduction to special relativity|relativistic]] equation.)<ref>
{{cite book
|first=Henok | last=A.
|title=Introduction to Applied Modern Physics
|page=76
|publisher=[[Lulu.com]]
|year=2002
|isbn=1-4357-0521-1
}}</ref>
 
==Importance==
 
The Stern–Gerlach experiment strongly influenced later developments in modern physics:
 
*In the decade that followed, scientists showed using similar techniques, that the nuclei of some atoms also have quantized angular momentum. It is the interaction of this nuclear angular momentum with the spin of the electron that is responsible for the [[hyperfine structure]] of the spectroscopic lines.
 
*In the 1930s, using an extended version of the Stern–Gerlach apparatus, [[Isidor Rabi]] and colleagues showed that by using a varying magnetic field, one can force the magnetic momentum to go from one state to the other. The series of experiments culminated in 1937 when they discovered that state transitions could be induced using time varying fields or [[radiofrequency|RF fields]]. The so-called '''[[Rabi oscillation]]''' is the working mechanism for the [[Magnetic Resonance Imaging]] equipment found in hospitals.
 
* [[Norman F. Ramsey]] later modified the Rabi apparatus to increase the interaction time with the field. The extreme sensitivity due to the frequency of the radiation makes this very useful for keeping accurate time, and it is still used today in [[atomic clock]]s.
 
* In the early sixties, Ramsey and [[Daniel Kleppner]] used a Stern–Gerlach system to produce a beam of polarized hydrogen as the source of energy for the hydrogen [[Maser]], which is still one of the most popular atomic clocks.
 
* The direct observation of the spin is the most direct evidence of quantization in quantum mechanics.
 
* The Stern–Gerlach experiment has become a paradigm of [[Measurement in quantum mechanics|quantum measurement]]. In particular, it has been assumed to satisfy [[Measurement in quantum mechanics#Wavefunction collapse|von Neumann projection]]. According to more recent insights, based on a quantum mechanical description of the influence of the inhomogeneous magnetic field,<ref>
{{cite journal
|first=M.O. |last=Scully |first2=W.E. |last2=Lamb |first3=A. |last3=Barut
|title=On the theory of the Stern–Gerlach apparatus
|journal=[[Foundations of Physics]]
|volume=17 |pages=575–583
|year=1987
|doi=10.1007/BF01882788
|issue=6
|bibcode = 1987FoPh...17..575S }}</ref> this can be true only in an approximate sense. Von Neumann projection can be rigorously satisfied only if the magnetic field is homogeneous. Hence, von Neumann projection is even incompatible with a proper functioning of the Stern–Gerlach device as an instrument for measuring spin.
 
==See also==
 
*[[Photon polarization]]
*[[Stern-Gerlach-Medaille]]
*[[German inventors and discoverers]]
 
==References==
{{reflist}}
 
==External links==
* [http://www.toutestquantique.fr/#spin Animation, applications and research linked to the spin] (Université Paris Sud)
 
==Further reading==
* {{cite journal
|last=Friedrich |first=B. |last2=Herschbach |first2=D.
|title=Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics
|journal=[[Physics Today]]
|volume=56 |page=53
|year=2003
|doi=10.1063/1.1650229
|issue=12
|bibcode = 2003PhT....56l..53F }}
*{{cite journal
|last=Reinisch |first=G.
|title=Stern–Gerlach experiment as the pioneer—and probably the simplest—quantum entanglement test?
|journal=[[Physics Letters A]]
|volume=259 |issue=6 |pages=427–430
|year=1999
|doi=10.1016/S0375-9601(99)00472-7
|bibcode = 1999PhLA..259..427R }}
*{{cite journal
|last=Venugopalan |first=A.
|title=Decoherence and Schrödinger-cat states in a Stern−Gerlach-type experiment
|journal=[[Physical Review A]]
|volume=56 |pages=4307–4310
|year=1997
|doi=10.1103/PhysRevA.56.4307
|issue=5
|bibcode = 1997PhRvA..56.4307V }}
*{{cite journal
|last=Hsu |first=B. |last2=Berrondo |first2=M. |last3=Van Huele |first3=J.-F.
|title=Stern-Gerlach dynamics with quantum propagators
|journal=[[Physical Review A]]
|volume=83 |pages=012109-1-12
|year=2011
|doi=10.1103/PhysRevA.83.012109
|issue=1
|bibcode = 2011PhRvA..83a2109H }}
*{{cite arxiv |eprint=1007.2435v1 |author1=Jeremy Bernstein |title=The Stern Gerlach Experiment |class=physics.hist-ph |year=2010}}
*[http://msc.phys.rug.nl/quantummechanics/stern.htm#Ions Use of ions]
 
==External links==
 
{{commons category|Stern–Gerlach experiment}}
 
*[http://www.if.ufrgs.br/~betz/quantum/SGPeng.htm Stern–Gerlach Experiment Java Applet Animation]
*[http://phet.colorado.edu/simulations/sims.php?sim=SternGerlach_Experiment Stern–Gerlach Experiment Flash Model]
* [http://galileo.phys.virginia.edu/classes/252/Angular_Momentum/Angular_Momentum.html Detailed explanation of the Stern–Gerlach Experiment]
*[http://plato.stanford.edu/entries/physics-experiment/figure13.html Image of experiment result]
*http://www.kip.uni-heidelberg.de/matterwaveoptics/teaching/archive/ws07-08/SternGerlach.pdf
 
{{DEFAULTSORT:Stern-Gerlach experiment}}
[[Category:Quantum measurement]]
[[Category:Foundational quantum physics]]
[[Category:Physics experiments]]
[[Category:Spintronics]]
[[Category:1922 in science]]

Latest revision as of 22:14, 25 November 2014

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