相关论文: Explicit Spin Coordinates

Spherical Harmonics, $Y_\ell^m(\theta,\phi)$, are derived and presented (in a Table) for half-odd-integer values of $\ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the…

The Fermion Spherical harmonics [$Y_\ell^{m}(\theta,\phi)$ for half-odd-integer $\ell$ and $m$ - presented in a previous paper] are shown to have the same eigenfunction properties as the well-known Boson Spherical Harmonics…

A classical circularly polarized electromagnetic wave carries angular momentum, and represents the classical limit of a photon, which carries quantized spin. It is shown that a very similar picture of a circularly polarized coherent wave…

Orbital angular momentum eigenfunctions are readily understood in terms of spherical harmonic wavefunctions. However, the quantum mechanical phenomenon of spin is often said to be mysterious and hard to visualize, with no classical…

The spherical harmonics $Y_{\ell m}(\theta,\varphi)$ are complex-valued functions on the surface of a sphere, and have found widespread application in physics and astronomy. Every physics students knows them from quantum mechanics and…

The azimuthal and magnetic quantum numbers of spherical harmonics $Y_{l}^{m}(\theta,\phi)$ describe quantization corresponding to the magnitude and $z$-component of angular momentum operator in the framework of realization of $su(2)$ Lie…

Cylindrically symmetric electron beams in spin polarization are reported for the first time. They are shown to be the eigen states of total angular momentum in the $z$ direction. But they are neither the eigen states of spin nor the eigen…

A simple real-space model for the free-electron wavefunction with spin is proposed, based on coherent vortices on the scale of h/mc, rotating at mc^2/h. This reproduces the proper values for electron spin and magnetic moment. Transformation…

We show that when an electron or photon propagates in a cylindrically symmetric waveguide, its spin angular momentum (SAM) and its orbital angular momentum (OAM) interact. Remarkably, we find that the dynamics resulting from this spin-orbit…

In semiconductors, spin-orbit effective magnetic fields, i.e., the Rashba and Dresselhaus fields, are used to control electron-spin polarization. This operation, however, destroys the electron-spin coherence, and the spin polarization is…

The angular momentum quantum number L of spherical harmonic Y_l_,_m based on an associated Legendre polynomial is nonnegative integer 0 1 2 ... and must never be a fraction. But the study in this paper found that the quantum number L…

We demonstrate that non-equilibrium electrons in thin nonmagnetic semiconductor layers or quantum dots can be fully spin polarized by means of simultaneous electrical spin injection and extraction. The complete spin polarization is achieved…

We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and…

Spherical Harmonic Gaussian type orbitals and Slater functions can be expressed using spherical coordinates or a linear combinations of the appropriate Cartesian functions. General expressions for the transformation coefficients between the…

The motion of a particle with a spin in spherical harmonic oscillator potential with spin-orbit interaction is studied. We have focus our attention on spatial motion of wave packets, giving a description complementary to motion of spin…

Interference of spin-up and spin-down eigenstates depicts spin rotation of electrons, which is a fundamental concept of quantum mechanics and accepts technological challenges for the electrical spin manipulation. Here, we visualize this…

Since the discovery a century ago, spin describing the intrinsic angular momentum of massive elementary particles has exposed its nature and significant roles in wide ranges of (relativistic) quantum phenomena and practical applications for…

We suggest a new spin orientation mechanism for localized electrons: $dynamic~electron~spin~polarization~provided~by~nuclear~spin~fluctuations$. The angular momentum for the electrons is gained from the nuclear spin system via the hyperfine…

Electrons have three quantized properties -- charge, spin, and Fermi statistics -- that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron…

We compute the leading and sub-leading spin effects through the second post-Newtonian order (2PN) in spherical harmonic modes of gravitational waveforms from inspiralling compact binaries in non-circular orbits with non-precessing…