L_+=hbar*e^(i*φ)*(∂/∂θ+i*cot(θ)*∂/∂φ)
L_-=hbar*e^-(i*φ)*(-∂/∂θ+i*cot(θ)*∂/∂φ)
ok, i got them squared away
how do i write cos(φ) in terms of L_+ and L_-?
also,
i would be interested in reading your thesis
cheers
nate
Homework Statement
Derive the general expression of 3rd-order perturbation energy for a
non-degenerate quantum system.
Homework Equations
for nth order we have
(Ho-Eo)|n>+(H'-E1)|n-1> -E2\n-2>-En|0>=0 (given)
also,
<0|0>=1,
<1|0> = <0|1>=0,
<0|2>=<2|0>=-1/2<1|1>...
should i rewrite the eigenenergy as E=L^2/(2*I)? (to show its dependence of total angular momentum)
also, how should i go about writing the cos(φ) into L+and or L- operators?
L+=Lx+i*Ly
L-=Lx-i*Ly
oops!
I need to move my last post to a different problem, but thank you nrqed (is
the qed stand for what i think it does ) i thought that the ladder ops would be
important for the states |l'm'>
let me see what i can work out
cheers
nate
got some of it! (i hope!)
ok, i assume my question is a tough one, or that no one really understands
what i am asking!
:biggrin:
here is what i have so far
1st i need B in spherical coordinates
aside from that i am using B=B0x+B0y+B0z in cartesian coordinates
say the B-field...
Homework Statement
Due to the modification of inner-shell electrons of a multi-electron system,
the outer shell electron can feel an effective electrostatic potential as
V(r)=-e^2/(4*π*eo*R)-lambda*(e^2/(4*π*eo*R^2)) ; 0<lambda≤1
Find the energy eigenvalues and wavefunctions of the...
u'in(a)≠u'out(a)
uout(a)=C*e^-(l*a) (simple enough)
since l=0, the Neumann function nl(ka)=-B*a*(cos(a)/a)
uin(a)=-B(cos(a)) ?
u'in(a)B*sin(a)
u'out(a)=-l*a*C*e^(-l*a)
now i use u'in(a)≠u'out(a) to solve for Vo?
can i get away with setting A=0 and D=0 like in the finite...
anyone still with me on this problem?
i need to find the solutions for 1st order perturbation for this (degenerate) system!
ouch!
I have as the eigenenergies E(l,m)=l(l+1)*hbar^2/(2*I)
now how do i use denegerate perturbation theory to solve for the 1st order
correction to an...
ok, let me try this again
H=-mu*B (this is the interaction energy between spin and B-field)
for a particle of spin 1/2, with magnetic moment mu=mu(s)*S
the Hamiltonian is h=1/2*m(p-q/c*A)^2-mu*B
B=BX+BY+BZ (where i need to put B into spherical coordinates)
so if i have the B-field in the...
so for r≥a the solutions are called modified spherical Bessel Functions (lol)
kl(kr) k^2=(2m|E|)/hbar^2
for boundary conditions (l=0)
r=a
(djl(Kr)/dr)/jl(Kr)|r=a- = (dkl(kr)/dr)/kl(kr)|r=a+
now since l=0, and j0(x)=sin(x)/x and k0(x)=e^-x/x (these are the solutions
that join together at...