Stern—Gerlach experiment

Another experiment that relates to the physical interpretation of the wave function was performed by O. Stem and W. Gerlach (1922). Their experiment is a dramatic illustration of a quantum-mechanical effect which is in direct conflict with the concepts of classical theory. It was the first experiment of a non-optical nature to show quantum behavior directly. 

Silver atoms, being paramagnetic, have a magnetic moment M. In a magnetic field B, the potential energy Fof each atom is 

Between the poles of the magnet, the magnetic field B varies rapidly in the x- 

The Stem-Gerlach experiment shows that the magnetic moment of each 

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The Stern-Gerlach experiment demonstrated that electrons have an intrinsic angular momentum in addition to their orbital angular momentum, and the unfortunate term electron spin was coined to describe this pure quantum-mechanical phenomenon. Many nuclei also possess an internal angular momentum, referred to as nuclear spin. As in classical mechanics, there is a relationship between the angular momentum and the magnetic moment. For electrons, we write... 

Stern-Gerlach experiment, 31 stibnite, 626 stiffness of bond, 92 STM, FI6, 189 Stock number, F30 stock solution, F58 stoichiometric coefficient,... 

Orbital angular momentum of an electron in an atom can be measured by the same type of Stern-Gerlach experiment described before for the measurement of electron spin. In this case it will be assumed to use a metal such as magnesium whose atoms have a total electron spin of zero. The magnetic moment... 

Let us consider this case in some detail. If collisions are eliminated in a molecular beam, it is possible to orient molecules (their figure axis) by removing the particles possessing unwanted orientation (analogous to the Stern-Gerlach experiment with a magnetic field). Then, classically, the interaction energy with external electric field is simply... 

This degeneracy is lifted in a magnetic field, for instance in a Stern-Gerlach experiment. 

The spinor that describes the spherical rotation satisfies Schrodinger s equation and specifies two orientations of the spin, colloquially known as up and down (j) and ( [), distinguished by the allowed values of the magnetic spin quantum number, ms = . The two-way splitting of a beam of silver ions in a Stern-Gerlach experiment is explained by the interaction of spin angular momentum with the magnetic field. 

THE FOURTH ELECTRONIC DEGREE OF FREEDOM The Stern-Gerlach Experiment... 

Figure 1 Schematic drawing of the Stern-Gerlach experiment.

The results of the Stern-Gerlach experiment were in complete contradiction to the classical interpretation and its predictions. Silver atoms turned out to possess a magnetic moment, but instead of a single, smeared-out distribution, two spots centered around Mup and Mdown were observed. Thus the magnetic moment of a silver atom is space-quantized by an inhomogeneous magnetic field, and this magnetic moment can adopt only two values, hz Hhl ... 

From our present standpoint, we know that the deflection of a silver atom in the Stern-Gerlach experiment is caused by the interaction of its electronic spin angular momentum S with an inhomogeneous magnetic field. The projection of S on the direction of this field, Ms, is quantized. For a silver atom, Ms can take two values +vjh and — h, where h is Planck s constant h over 2ji and adopts a value of 1.054571596 x 10-34 Js in cgi units. 

Let us first consider the normal Zeeman effect, which applies to transitions between electronic states with zero total spin magnetic moment, so-called singlet states. Like the projection Ms of S in the Stern-Gerlach experiment, the projection Ml of the spatial angular momentum L is space quantized in the external magnetic field. We shall describe the quantization of the spatial angular momentum by means of quantum mechanical methods in detail later. Suffice it to say that each state with spatial angular momentum quantum number L splits into 2L + 1 components, i.e., a P state (L = 1) splits into three components with... 

The conceptual simplicity of the Stern-Gerlach experiment, coupled with the directness of its results, provided commanding evidence for the quantum theory. I. I. Rabi was a graduate student at Columbia University when the Stern results were announced. The Stern experiment changed forever Rabi s thinking about quantum mechanics. This convinced me once and for all, Rabi said later, that an ingenious classical mechanics was out and that we had to face the fact that the quantum phenomena required a completely new orientation. ... 

Shortly after the results of the Stern-Gerlach experiment appeared in the scientific literature. Stern received an invitation to join the faculty at the University of Hamburg, where, over the period 1922 to 1933, he continued his experimental work. In 1932, Stern decided to adapt the molecular beam method to a daunting experiment to measure the magnetic moment of the proton, the nucleus of the hydrogen atom. Joining him is this endeavor was Otto Robert Frisch. 

Fig. 3.17 Stern-Gerlach experiment for H atoms in their ground state.

The Stern-Gerlach experiment demonstrates that the electron has a property called spin, which leads to a magnetic dipole moment. Spin is quantized with only two allowed values described by the quantum number m. Complete determination of the quantum state of the electron required values for all four quantum numbers (n, , m, m. ... 

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