SUSY
An abbreviation for Super-Symmetrical Quantum mechanics.Consider a
QM system with
Hamiltonian H and potential V(x) such that H |Ψ> = E |Ψ>We define a new Hamiltonian
H1 in terms of potential
V1(x) which is offset by the
zero point energy so that:H1 |0> = 0 ie the enegy of the ground state of H1 is zero.We define this Hamiltonian in terms of generalized raising and lowering operators A and A dagger such that:H1 = A_dag A = (
p^2/
2m) + V1(x)A = (ip/root(2m)) + W'(x)Where W(x) is the super potential.The potential V1(x) can be constructed from the superpotential:V1(x) = W'(x)^2 - (ћ/root(2m))W"(x)If we know the H1 ground state Ψ_0(x) then we can derive:Ψ_0(x) ~ exp(-root(2m)W(x)/ћ)Which can be used to find the superpotential W(x)From this superpotential we can derive the partnerpotential
V2(x) where:V2(x) = W'(x)^2 - (ћ/root(2m))W"(x)which has associated Hamiltonian
H2 = A A_dag = (p^2/2m) + V2(x)This partner potential may allow H2 to have an eigenspectrum which is easier to find. Once this is found we can go from the
nth energy level of H2 to the (
n+1)th level of H1 by simply applying the A_dag operator. This means we can find the first excited state of H1 by applying A_dag to the ground state of H2.Note: I wrote this while in class and the prof was talking about some really complex shit I wasn't paying attention to so now
I'm fucked for the exam next week.But
sugondese amirite?At least we still got us a
woodshed!
Susie
by Greatest Lax Goalie Ever! on Feb 25, 2011 02:46:01
One of the coolest girls alive. Always fun to be around. Make great
sisters and friends.
Susies are usually funny, smart, nice and
energetic. Crazy at times. Throws great parties and is overall one of the best. If you know one or have one as a sister consider yourself lucky!
Susie
by ispeakthetruth3.14 on Feb 11, 2012 18:28:13
Susies are simply sweet. Girls with this name are classy, intelligent, adventurous, dreamers, hard working,
selfless, driven, romantic and funny. Susies make the best guests because they're respectful of
other peoples space.
Example:
mother
to son: Your new girlfriend is really lovely. She even helped me
cook dinner. She must be a Susie.
Susi
by Susi master on May 27, 2021 01:38:26
SUSI is a term created in Norway originated by a group of yuths in
Fredrikstad , the word went from one person to another thats how it became popular. The term means look at your clothes like they look nice hella
drippy.