;ò ó—Fc@svdZdklZdefd„ƒYZ[dklZdefd„ƒYZ[dklZdfd „ƒYZ d S( sKAtomic energy levels. $Id: atomic.py,v 1.2 2007/03/08 23:22:35 eddy Exp $ (s PolynomialsLaguerrecBsUtZeiZdklZdklZeed„Z[[eddƒd„Z RS(N(shcf(s factorialc Cs|djp0||jp#|t|ƒjp|t|ƒjotd||ƒ‚ndg|}|||d|ƒ||df\}}}xD||jo6|d}|||<|||d|||}q”W|djpt ‚|i t t |t|ƒƒd„|ƒƒdS(Nis5Laguerre(n, b) is defined for natural n, b with n > bicCs||S(N(sxse(sxse((s(/home/eddy/.sys/py/study/chemy/atomic.pyss(sbsnsints ValueErrorsfsplingsjslastsLsAssertionErrorsselfs_Laguerre__upinitsmapsapplyshcfstuple( sselfsnsbshcfsplingslastsfsjsL((s(/home/eddy/.sys/py/study/chemy/atomic.pys__init__ s@ .   #iicCs||didSdS(Nif0.5(sselfslinearsGamma(sselfsigslinear((s(/home/eddy/.sys/py/study/chemy/atomic.pys_lazy_get_scale_s( s__name__s __module__s Polynomials__init__s_Laguerre__upinitsstudy.maths.naturalshcfsstudy.maths.Pascals factorials_lazy_get_scale_(((s(/home/eddy/.sys/py/study/chemy/atomic.pysLaguerres    (sLazysRadialcBs,tZd„Zd„Zd„Zd„ZRS(NcCs>t||ƒ|d|f\|_|_d|d|_dS(Nf1.0ii(sLaguerresnsbsZsselfs _Radial__polys _Radial__fracs degeneracy(sselfsnsbsZ((s(/home/eddy/.sys/py/study/chemy/atomic.pys__init__$s)cCs|iid|idSdS(Nif1.5(sselfs _Radial__polysscales _Radial__frac(sselfsig((s(/home/eddy/.sys/py/study/chemy/atomic.pys_lazy_get_scale_(scCs|id SdS(Ni(sselfs _Radial__frac(sselfsig((s(/home/eddy/.sys/py/study/chemy/atomic.pys_lazy_get_Energy_+scCs0||i}|id|ƒ|i|iSdS(Ni(srsselfs _Radial__fracs _Radial__polysexpsscale(sselfsr((s(/home/eddy/.sys/py/study/chemy/atomic.pys__call__.s (s__name__s __module__s__init__s_lazy_get_scale_s_lazy_get_Energy_s__call__(((s(/home/eddy/.sys/py/study/chemy/atomic.pysRadial#s   (s SphericalsOrbitcBs&tZdd„Zd„Zd„ZRS(NicCsˆ|djp|t|ƒjotd|ƒ‚nt|||ƒ|_t||ƒ|_ ||||f\|_|_ |_ |_dS(sïInitialize a dimensionless quantum orbit in a Coulomb field. Required parameters: n - shell number; natural b - total angular momentum number; natural < n j - angular momentum component about coordinate axis; integer between minus b and b. Optional argument: Z - atomic number of atom (charge on nucleus); positive integer. Describes a potential orbit of a lone electron about a nucleus of atomic number Z. is*Atomic number should be a positive integerN( sZsints ValueErrorsRadialsnsbsselfs_Orbit__radials Sphericalsjs_Orbit__angularsl(sselfsnsbsjsZ((s(/home/eddy/.sys/py/study/chemy/atomic.pys__init__8s  cCs|iiSdS(sIn units of the Rydberg energyN(sselfs_Orbit__radialsEnergy(sselfsig((s(/home/eddy/.sys/py/study/chemy/atomic.pys_lazy_get_Energy_OscCs!|i||ƒ|i|ƒSdS(sÖReturns dimensionless field probability at specified location. The radial co-ordinate, r, should be a dimensionless Quantity() obtained by dividing true radius by the Bohr radius, hbar / (mass * alpha * c) where the mass should really be a reduced mass, given by 1/mass = 1/electron.mass + 1/nucleus.mass. The returned field value should be divided by a factor of this Bohr radius to the power 1.5 to get a quantity whose squared modulus, when integrated over a volume, yields the probability of finding the electron in that volume. Alternatively, skip that scaling and do your integration in co-ordinates which use the Bohr radius as unit of length. N(sselfs_Orbit__angularsphisthetas_Orbit__radialsr(sselfsrsphistheta((s(/home/eddy/.sys/py/study/chemy/atomic.pys__call__Ss (s__name__s __module__s__init__s_lazy_get_Energy_s__call__(((s(/home/eddy/.sys/py/study/chemy/atomic.pysOrbit7s  N( s__doc__sstudy.maths.polynomials PolynomialsLaguerresstudy.value.lazysLazysRadialsstudy.maths.Legendres SphericalsOrbit(s SphericalsLazysLaguerresOrbitsRadials Polynomial((s(/home/eddy/.sys/py/study/chemy/atomic.pys?s