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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!
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!
Guy one: Look at that physicist fuck over there doing SUSY.
Guy two: Damn straight brother I hear SUSY sucks a lot.
Guy one: Hell yeah she does!
Guy two: Damn straight brother I hear SUSY sucks a lot.
Guy one: Hell yeah she does!
by Migdal Kadanoff April 26, 2019
Aug 11 Word of the Day
A phrase to describe someone who is cognitively degenerating. Synonym of "going off the deep end". Can have varying degrees of severity.
Reference to the song "Hey You" by Pink Floyd. The line "and the worms ate into his brain" makes no sense in an otherwise linear and literal narration throughout the lyrics.
Reference to the song "Hey You" by Pink Floyd. The line "and the worms ate into his brain" makes no sense in an otherwise linear and literal narration throughout the lyrics.
"My boyfriend has a total case of brain worms. He told me the cat was bugged so the Feds could listen in on us having sex..."
or
"You totally stumbled over that entire sentence. Can't speak English all of a sudden? What, do you have brain worms?"
or
"You totally stumbled over that entire sentence. Can't speak English all of a sudden? What, do you have brain worms?"
by _Jez_ October 03, 2009