Trajectories and causal phase-space approach to relativistic quantum mechanics

1987 ◽  
Vol 17 (5) ◽  
pp. 531-548 ◽  
Author(s):  
P. R. Holland ◽  
A. Kyprianidis ◽  
J. P. Vigier
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Space Approach

scholarly journals Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

2015 ◽  
Vol 70 (8) ◽  
pp. 619-627 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Hypergeometric Functions ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

AbstractWe consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

Stochastic microcausality in relativistic quantum mechanics

1984 ◽  
Vol 14 (9) ◽  
pp. 883-906 ◽  
Author(s):  
D. P. Greenwood ◽  
E. Prugovečki
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

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