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I would like to use Mathematica to solve a system of linear equations with lots of unknowns(729 unknowns), the unknowns are tensor components of curvature tensors arising from a differential geometry problem. Editable and set the value to True, search Saveable and set the value to True and close the Option Inspector 5. The simulation software is used across multiple fields of study and purpose that includes engineering, scientific research, and field computing. The latest volley in the contest comes from Wolfram Research's Mathematica 7.0. Beautifully Render* your Graphic3D and Shown or Manipulate right in the Front End (without Export to.

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Probability of Quantum Tunnelling in Nucleation (natural units)

Hey there. I'm a 24 y/o lad, and i'm currently writing my thesis. I'm losing my mind over this problem that i'm gonna explain, just because natural units:
My thesis talks about the theoretical possibility of reaching a new stable state of matter composed by strange matter, starting from hadronic matter. This phase transition would happen through the nucleation process.
The system i'm studying has a potential U(r)=-a*r^3+b*r^2+c*r^5 where a,b,c are parameters which i'm changing during my calculations; this potential is expressed in MeV.
This potential is basically a double well with a barrier in the middle and through Wolfram Mathematica i have to calculate the probability of quantum tunnelling through this barrier.
I'm gonna explain briefly the formulas i'm using for this type of calculation:
I have to calculate the eigenvalue of the ground state using the Bohr quantization condition I(E0)=3/2*pi*hbar where I(E)=integral from 0 to r- Sqrt(2*M(r)(E-U))dr where r- is the inferior classical turning point (i'm using the WKB approximation), so i'm giving a value to E0, calculating the integral then finding r- and i do this until i find the correct values for r- and E0 that satisfy Bohr condition.
Once i've done this, i have to calculate another action integral A(E)=integral from r- to r+ Sqrt(2*M(r)(U-E))dr where r+ is the superior classical turning point, i have to calculate then A(E0) (with Mathematica i just put E0 in the int.) and the final formula for the tunnelling probability is p0=exp(-a/hbar).
Getting to the point, the probability that i find is incredibly small. The problem i'm facing is about natural units, i'm forgetting some hbar or c somewhere and for almost 2 weeks i can't find the answer.
M(r) is the mass of the droplet and it's in MeV. So in the integral I(E), dimensionalment speaking, i have sqrt(MeV*MeV)*fm where fm comes from the dr. Thus the integral is MeV*fm. By the way, an action is an energy times a time, so i would have MeV*fm/c. At this point i thought that the factor 1/c comes from the mass of the droplet since the mass is MeV/c^2 and, under square root, it comes out 1/c.
But if i use the mass M(r) in MeV and not MeV/c^2, for the Bohr condition, since my integral is in MeV*fm, i have to multiply the second member (3/2*pi*hbar) times c, so i'm getting 3/2*pi*hbar*c=3/2*pi*200 Mev*fm
Is this right?
Last but not least problem, since i think it's the bigger one, i have to calculate A(E0). Same argument, A(E0) is in MeV*fm, so when i put it in p0=exp(-A/hbar) i have to consider the factor 1/c, so if i use A in Mev*fm, which i do, i have 1/hbar*1/c which is 1/200 Mev*fm and in the end p0=exp(-A[MeV*fm]/200 MeV*fm) and everything seems beautiful and fine.
Sadly this is not Candy Land, and numerically the probability is incredibly small (order of 10^-30 average), but i cannot understand where i'm wrong with units of measurements. This is so frustrating, i have no more ideas left, i tried everything. Does anybody notice an error in my reasoning? You will make my day.
Thank you for your attention, and have a good day.
submitted by Zanfo96 to quantummechanics

Wolfram's Mathematica 10 connects math to the cloud

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