Zobrazeno 1 - 10
of 37
pro vyhledávání: '"McNamara, Daniel J."'
In this paper, we use Clifford algebra $Cl_{2,0}$ to find the 2D orbit of Hydrogen electron under a Coulomb force and a perturbing circularly polarized electric field of light at angular frequency~$\omega$, which is turned on at time $t = 0$ via a un
Externí odkaz:
http://arxiv.org/abs/2410.00056
Autor:
Perez, Uzziel, Ang, Angeleene S., Sugon Jr., Quirino M., McNamara, Daniel J., Yoshikawa, Akimasa
We studied the orbit of an electron revolving around an infinitely massive nucleus of a large classical Hydrogen atom subject to an AC electric field oscillating perpendicular to the electron's circular orbit. Using perturbation theory in geometric a
Externí odkaz:
http://arxiv.org/abs/1507.04509
We used Geometric Algebra to compute the paths of skew rays in a cylindrical, step-index multimode optical fiber. To do this, we used the vector addition form for the law of propagation, the exponential of an imaginary vector form for the law of refr
Externí odkaz:
http://arxiv.org/abs/1504.02906
We use the vector wedge product in geometric algebra to show that Poisson commutator brackets measure preservation of phase space areas. We also use the vector dot product to define the Poisson anticommutator bracket that measures the preservation of
Externí odkaz:
http://arxiv.org/abs/0812.2979
We propose that the height-angle ray vector in matrix optics should be complex, based on a geometric algebra analysis. We also propose that the ray's 2x2 matrix operators should be right-acting, so that the matrix product succession would go with lig
Externí odkaz:
http://arxiv.org/abs/0812.0664
We represent vector rotation operators in terms of bras or kets of half-angle exponentials in Clifford (geometric) algebra Cl_{3,0}. We show that SO_3 is a rotation group and we define the dihedral group D_4 as its finite subgroup. We use the Euler-R
Externí odkaz:
http://arxiv.org/abs/0811.3680
We derive the paraxial meridional ray tracing equations from the unified reflection-refraction law using geometric algebra. This unified law states that the normal vector to the interface is a rotation of the incident ray or of the refracted ray or o
Externí odkaz:
http://arxiv.org/abs/0810.5224
We list the subgroups of the basis set of Cl_{3,0} and classify them according to three criteria for construction of universal Clifford algebras: (1) each generator squares to +1 or -1, (2) the generators within the group anticommute, and (3) the ord
Externí odkaz:
http://arxiv.org/abs/0809.0351
We derive Copernicus's epicycles from Newton's gravitational force law by assuming that a planet's orbit is a perturbed circular orbit, with the perturbation defined to be co-rotating with the said orbit. We substitute this orbit expression into Newt
Externí odkaz:
http://arxiv.org/abs/0807.2708
In this paper, we define energy-momentum density as a product of the complex vector electromagnetic field and its complex conjugate. We derive an equation for the spacetime derivative of the energy-momentum density. We show that the scalar and vector
Externí odkaz:
http://arxiv.org/abs/0807.1382