方程的解我们很熟悉,是球谐函数(Spherical harmonics function) Y_{lm}(\theta, \varphi)=(-1)^m \sqrt{\frac{(2l+1)}{l\hbar} \frac{(l-m)!}{(l+m)!}} \ P_l^m(\cos \theta) \, e^{im\varphi} 其中P_l^m(\cos \theta) 是连带勒让德函数(Associated Legendre functions)径向...
The maximum degeneracy is reached at a superdeformed hemispheroidal prolate shape whose magic numbers are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator. This remarkable property suggests an increased stability of such a distorted shape of deposited clusters ...
The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunction is performed through the introduction of non-local ladder operators. By exploring the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues for the angular ...
Our polytope-based cat codes consist of sets of points with large separation that, at the same time, form averaging sets known as spherical designs. We also recast concatenations of Calderbank–Shor–Steane codes with cat codes as quantum spherical codes, which establishes a method to ...
The results are compared with some numerical calculations for spherical rectangular well and an extension to many-electron atoms is also presented. The effect of breaking degeneracy and of ordering energies of H in a different way than in the case of many-electron systems is broadly discussed. (...
[100]Orthonormality of spherical harmonics.zh_en 17:57 [101]Effective potential and boundary conditions at r=0.zh_en 14:29 [102]Hydrogen atom two-body problem.zh_en 25:05 [103]Center of mass and relative motion wavefunctions.zh_en ...
The results of such analysis suggest that spherical masses give rise to the highest amount of generated entanglement. The Newtonian gravitational energy of this setting is the same as if the two objects were point-like masses, that is Hg = −Gm2 / (L + xB − xA), ...
I noticed the schematic occurrence of selection rules from integrals over spherical harmonics a pretty long time ago, even before I knew the precise connection to Heisenberg. It was my first hint [Fingerzeig] for deciphering the mysterious matrix elements.Footnote 67 This is the first instance we...
It has the incredible property that if the spherical mass is compact enough then spacetime will be so strongly curved that nothing will be able to escape (at least from the perspective of GR; we believe that there are corrections to this when you add quantum mechanics to the mix.) ...
In the Supplementary Note 1 an account of this procedure is given for O(N) symmetric models with long-range couplings in 1-dimension, where the Hartee–Fock method becomes exact in the large-N limit49,50,51 (the so-called spherical model52,53). In the last few decades, O(N) field ...