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The Quantum-Mechanical Description of a Relativistic Electron in a Constant and Homogeneous Magnetic Field.

David Allyn White

Jan 1, 19720 citations

Relativistic Wave Mechanics of Electrons Deflected by a Magnetic Field

MILTON S. PLESSET

It is shown that the relativistic wave equation for electrons in a uniform magnetic field leads to the same wave function as that already deduced by Page from the non-relativistic equation. As in the latter case the motion at right angles to the field is quantized.An expression is found for the current density from the relativistic wave equation. The relativistic expression differs from the non-relativistic only by a constant factor which does not affect the calculation of the mean radii of curvature of the electron current.Hence, for the relativistic case, as for the non-relativistic, the mean radius of curvature is less than that expected on the classical theory. It follows that the classical relativistic relation between $\frac{\ensuremath{\epsilon}}{\ensuremath{\mu}}$ and the mean radius of curvature upon deflection gives a value of $\frac{\ensuremath{\epsilon}}{\ensuremath{\mu}}$ which is too large.It is shown that the relativistic wave equation for electrons in a uniform magnetic field leads to the same wave function as that already deduced by Page from the non-relativistic equation. As in the latter case the motion at right angles to the field is quantized.An expression is found for the current density from the relativistic wave equation. The relativistic expression differs from the non-relativistic only by a constant factor which does not affect the calculation of the mean radii of curvature of the electron current.Hence, for the relativistic case, as for the non-relativistic, the mean radius of curvature is less than that expected on the classical theory. It follows that the classical relativistic relation between $\frac{\ensuremath{\epsilon}}{\ensuremath{\mu}}$ and the mean radius of curvature upon deflection gives a value of $\frac{\ensuremath{\epsilon}}{\ensuremath{\mu}}$ which is too large.

Physical ReviewDec 15, 193020 citations

Paraxial wave function and Gouy phase for a relativistic electron in a uniform magnetic field

Liping Zou, Pengming Zhang, Alexander J Silenko

Abstract A connection between relativistic quantum mechanics in the Foldy–Wouthuysen representation and the paraxial equations is established for a Dirac particle in external fields. The paraxial form of the Landau eigenfunction for a relativistic electron in a uniform magnetic field is determined. The obtained wave function contains the Gouy phase and significantly approaches the paraxial wave function for a free electron.

arXiv:2003.04717Journal of Physics G Nuclear and Particle PhysicsFeb 28, 202012 citations

Wave function of an electron in a magnetic field in the rotator approximation

B. V. Kholomai

Russian Physics JournalJan 1, 19770 citations

Relativistic quantum mechanics of electrons

T. P. Das

Harper & Row eBooksJan 1, 197383 citations

Statistical Mechanics of the Finite Heisenberg Model. I

Chikao Kawabata, Masuo Suzuki

The eigen-functions and eigen-values of finite three-dimensional Heisenberg models with anisotropy constant as a parameter (spin=1/2) were obtained exactly with the aid of group theoretical technique and by using a high speed computer. The calculated eigenvalues are identical with those obtained by Serber and Dresselhaus for the isotropic simple cubic 2×2×2 lattice. However, it was found that some terms in their full expressions were to be corrected. The zeros of the partition function of the above 2×2×2 lattice have been investigated as functions of the anisotropy parameter both in the complex temperature plane and in the complex magnetic field plane. Thermodynamic functions such as energy, specific heat, magnetization, and susceptibility have been numerically computed for these finite system.The eigen-functions and eigen-values of finite three-dimensional Heisenberg models with anisotropy constant as a parameter (spin=1/2) were obtained exactly with the aid of group theoretical technique and by using a high speed computer. The calculated eigenvalues are identical with those obtained by Serber and Dresselhaus for the isotropic simple cubic 2×2×2 lattice. However, it was found that some terms in their full expressions were to be corrected. The zeros of the partition function of the above 2×2×2 lattice have been investigated as functions of the anisotropy parameter both in the complex temperature plane and in the complex magnetic field plane. Thermodynamic functions such as energy, specific heat, magnetization, and susceptibility have been numerically computed for these finite system.

Journal of the Physical Society of JapanJan 1, 197014 citations

Eigen value and eigen function for electron in magnetic field using relativistic quantum mechanics

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