Physical Review

The Zeeman Effect of the Symmetrical Top according to Wave Mechanics

E. U. Condon

Published Dec 1, 1927• 14 citations

Abstract

The alteration of the quantum-theoretical energy levels of a symmetrical top due to the action of a magnetic field on a charge which is fixed to the top, is investigated by means of the perturbation theory of the wave mechanics. The final formula for the change in the energy levels is given below in Eq. (10).

DOI: 10.1103/physrev.30.781

Related papers

Experimental Study of Zeeman Light Shifts in Weak Magnetic Fields

Claude N. Cohen-Tannoudji, J. Dupont-Roc

Physical Review AFeb 1, 1972265 citations

The Quantized Hamiltonian for a Charged Particle in an Electromagnetic Field

Floyd L. Williams

Progress in mathematical physicsJan 1, 20030 citations

Theory of Doublet Spectra under Magnetic Perturbation

S. Sengupta

Jul 1, 19490 citations

The Symmetrical Top in the Undulatory Mechanics

R. de L. Kronig, Isidor Isaac Rabi

Physical ReviewFeb 1, 192777 citations

The second level amendment of the energy and the wave function in the degenerate perturbation theory

Wei Ming

According to the way of the second level amendment of the energy and the wave function in the non-degenerate perturbation theory,the second level amendment of the energy and the wave function are induced in degenerate perturbation theory, which forms the formula of the second level amendment.

Journal of Guizhou Normal UniversityJan 1, 20060 citations

Comparison Between Normal Zeeman Effect and Abnormal Zeeman Effect

Zhen Zhou

This paper Compares the normal Zeeman effect and abnormal Zeenman effect by three aspects:the strong or weak magnetic field,the value of Lande g-factor and the quantum mechanics perturbation theory and reveals the distinction connection between normal Zeeman effect and abnormal Zeenman effect.

Journal of Hubei Institute for NationalitiesJan 1, 20040 citations

Physical Review

The Zeeman Effect of the Symmetrical Top according to Wave Mechanics

E. U. Condon

Published Dec 1, 1927• 14 citations

Publisher

Abstract

DOI: 10.1103/physrev.30.781

Related papers

Experimental Study of Zeeman Light Shifts in Weak Magnetic Fields

Claude N. Cohen-Tannoudji, J. Dupont-Roc

According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian ${\mathcal{H}}_{e}$ which depends on the polarization and spectral profile of the incident light. In order to check the structure of ${\mathcal{H}}_{e}$ , we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to ${\mathcal{H}}_{e}$ . We have been able to obtain experimentally in the ground state of $^{199}\mathrm{Hg}$ , $^{201}\mathrm{Hg}$ , and $^{87}\mathrm{Rb}$ , Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of ${\mathcal{H}}_{e}$ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian ${\mathcal{H}}_{e}$ which depends on the polarization and spectral profile of the incident light. In order to check the structure of ${\mathcal{H}}_{e}$, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to ${\mathcal{H}}_{e}$. We have been able to obtain experimentally in the ground state of $^{199}\mathrm{Hg}$, $^{201}\mathrm{Hg}$, and $^{87}\mathrm{Rb}$, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of ${\mathcal{H}}_{e}$ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.

Physical Review AFeb 1, 1972265 citations

The Quantized Hamiltonian for a Charged Particle in an Electromagnetic Field

Floyd L. Williams

Electric fields and magnetic fields exert a manifest influence, or effect, on the energy levels of an atom. These effects, revealed for example by the splitting of spectral lines, are called Stark and Zeeman effects, respectively. The Stark effect (first observed by Johannes Stark in 1913) plays an important role, for example, in theoretical attempts to understand the formation of molecules from atoms. Our interest will be in the Zeeman effect—especially as we consider the notion of “spin,” and spin wave functions in the next chapter, particularly in Section 9.3 there. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.Electric fields and magnetic fields exert a manifest influence, or effect, on the energy levels of an atom. These effects, revealed for example by the splitting of spectral lines, are called Stark and Zeeman effects, respectively. The Stark effect (first observed by Johannes Stark in 1913) plays an important role, for example, in theoretical attempts to understand the formation of molecules from atoms. Our interest will be in the Zeeman effect—especially as we consider the notion of “spin,” and spin wave functions in the next chapter, particularly in Section 9.3 there. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Progress in mathematical physicsJan 1, 20030 citations

Theory of Doublet Spectra under Magnetic Perturbation

S. Sengupta

The problem of a spinning electron moving round the nudeu.s in the piesence of an external magnetic held ha.sbeen considered from the wave-statistical point of view.The general expressions for energies and wave functions in any held strength have l)een obtained.The problems of no field, weak field (Zeeman effect) and strong field (Paschen-Back effect) are considered as .specialcases.The resnlt.s for the no field case are identical with tho.se obtained in the earlier paper (Kar and Sengnpta.uj'ig).Other results also agree with the well-known spectro,scopic formulae,The problem of a spinning electron moving round the nudeu.s in the piesence of an external magnetic held ha.sbeen considered from the wave-statistical point of view.The general expressions for energies and wave functions in any held strength have l)een obtained.The problems of no field, weak field (Zeeman effect) and strong field (Paschen-Back effect) are considered as .specialcases.The resnlt.s for the no field case are identical with tho.se obtained in the earlier paper (Kar and Sengnpta.uj'ig).Other results also agree with the well-known spectro,scopic formulae,

Jul 1, 19490 citations

The Symmetrical Top in the Undulatory Mechanics

R. de L. Kronig, Isidor Isaac Rabi

Schr\"odinger's method for determining the energy levels of an atomic system is applied to the case of the symmetrical top (moment of inertia about axis of symmetry $C$ , the other one $A$ ). The energy values are found to be ${W}_{\mathrm{jn}}=\frac{{h}^{2}}{8{\ensuremath{\pi}}^{2}}\left[\frac{1}{A}j(j+1)+\left(\frac{1}{C}\ensuremath{-}\frac{1}{A}\right){n}^{2}\right]$ in agreement with the result obtained by Dennison from the matrix mechanics. The quantum numbers $j$ and $n$ must be integers restricted by $0\ensuremath{\leqq}j$, $|n|\ensuremath{\leqq}j$, while half-integral values are not permissible. The intensities of transitions are also calculated.Schr\"odinger's method for determining the energy levels of an atomic system is applied to the case of the symmetrical top (moment of inertia about axis of symmetry $C$, the other one $A$). The energy values are found to be ${W}_{\mathrm{jn}}=\frac{{h}^{2}}{8{\ensuremath{\pi}}^{2}}\left[\frac{1}{A}j(j+1)+\left(\frac{1}{C}\ensuremath{-}\frac{1}{A}\right){n}^{2}\right]$ in agreement with the result obtained by Dennison from the matrix mechanics. The quantum numbers $j$ and $n$ must be integers restricted by $0\ensuremath{\leqq}j$, $|n|\ensuremath{\leqq}j$, while half-integral values are not permissible. The intensities of transitions are also calculated.

Physical ReviewFeb 1, 192777 citations

The second level amendment of the energy and the wave function in the degenerate perturbation theory

Wei Ming

Journal of Guizhou Normal UniversityJan 1, 20060 citations

Comparison Between Normal Zeeman Effect and Abnormal Zeeman Effect

Zhen Zhou

Journal of Hubei Institute for NationalitiesJan 1, 20040 citations

{\mathcal{H}}_{e}

which depends on the polarization and spectral profile of the incident light. In order to check the structure of

{\mathcal{H}}_{e}

, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to

{\mathcal{H}}_{e}

. We have been able to obtain experimentally in the ground state of

^{199}\mathrm{Hg}

^{201}\mathrm{Hg}

, and

^{87}\mathrm{Rb}

, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of

{\mathcal{H}}_{e}

can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.

Schr\"odinger's method for determining the energy levels of an atomic system is applied to the case of the symmetrical top (moment of inertia about axis of symmetry

C

, the other one

A

). The energy values are found to be ${W}_{\mathrm{jn}}=\frac{{h}^{2}}{8{\ensuremath{\pi}}^{2}}\left[\frac{1}{A}j(j+1)+\left(\frac{1}{C}\ensuremath{-}\frac{1}{A}\right){n}^{2}\right]$ in agreement with the result obtained by Dennison from the matrix mechanics. The quantum numbers

j

and

n

must be integers restricted by $0\ensuremath{\leqq}j$, $|n|\ensuremath{\leqq}j$, while half-integral values are not permissible. The intensities of transitions are also calculated.