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    Machine accuracy vs. smallest representable number vs. smallest normalized number

    Homework Statement "Explain the difference between the machine accuracy, the smallest representable number, and the smallest normalized number in a floating point system". Homework Equations There is the bit-representation of floating numbers: (-1)^S * M * b^(E-e), using the fact that we can...
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    P+p -> p + (anti)p

    Thanks a bunch everyone! This discussion was really useful for me, and I hope a few others. Vanadium: Thanks for confirming the invariant momentum approach.. I was getting worried! And I finally found the proper way of calculating the velocity between the two frames :) So things like KE...
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    P+p -> p + (anti)p

    Hi PAllen, I'm guessing there's a square root around the denominator? Do you get the velocity from relativisitc momentum? Why is m(\gamma -1) needed? Are you using KE = E-mc^2 ? I'm studying for a test and it'd be nice to clarify this problem now :) Thanks for the input!
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    P+p -> p + (anti)p

    Bill_K: Can you please let me know how you got to this answer? Thanks..
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    P+p -> p + (anti)p

    Vanadium: Thank you... I was actually starting to think the same. There is one little problem: when I calculate the boost and calculate the momentum in the proton rest frame using the boost I get something different, I get 15.869 GeV. Here are my equations: y is the boost, p'_z =...
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    P+p -> p + (anti)p

    Correction: Sorry, I meant (P^\mu)^2 is an invariant..
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    P+p -> p + (anti)p

    PAllen: Thanks for the reminder! So I can find the boost using the ratio of energy and z-momentum, and supposing y is my boost, the energy in the lab frame would be: E' = E cosh(y) + p^z sinh y Is this correct? Nugatory, Bill_K, PAllen: Thanks for all of your input. I've thought of...
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    P+p -> p + (anti)p

    Hi Nugatory! Thanks for suggesting this reaction! It seems to conserve what it has to conserve (charge, baryon number). When I use the same calculation steps as I did originally, and assume the minimum required momentum for the incoming particle is when all outgoing particles have zero...
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    P+p -> p + (anti)p

    p+p --> p + (anti)p Hi everyone, I'm looking at the following problem from C. Bertulani's Ch.1, Problem 6. The problem statement is: "Using relativistic expressions for momentum and energy conservation, show that a proton must have energy greater than 5.6 GeV to produce a proton-antiproton...
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    Can an even number of Fermions be a Bosonic system?

    Hi everyone, I've just done a problem where we are dealing with two protons with the same spin directions and the system is treated as a fermionic system. I always had the notion that two (or an even number of) fermions, for opposite spin perhaps, act as bosons. Is this true? If so, when...
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    Why does vacuum have energy?

    Thanks everyone for your helpful replies! I think my thinking of the "vacuum" was naive as you have pointed out.. I was thinking of a box of "nothing" having some choosen base energy which we call the zero energy, and with this idea I wasn't sure why taking a larger box would have an even...
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    Why does vacuum have energy?

    Hello Everyone, I've been asked to work out a problem about vacuum energy <0|H|0> where H is the energy density of harmonic oscillator. When I integrate this expectation value over space of finite dimensions L, I get that the expectation value for the vacuum energy scales as L^3 . Does...
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    Why does Klein-Gordon's equation not obey quantum mechanics?

    Bill_K, thank you very much for your explanation!
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    Why does Klein-Gordon's equation not obey quantum mechanics?

    Thank you very much for the wake-up call on the 4-vector notation! Regarding the time-dependence, I understand the point made now, thank you. However, how would having an equation of motion which is first order in time solve this problem of the time dependence in the probability? Or, why does a...
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    Why does Klein-Gordon's equation not obey quantum mechanics?

    Hello Everyone, I was reading in Srednicki's QFT book, Chapter 1 and he was explaining why the Klein-Gordon equation doesn't obey quantum mechanics. He said the fact that the time derivative is second order means it disobey's Shrodinger's equation which is first order in the time derivative...
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    Transformation function from ground state -> nth energy state, force applied, HO

    Thank you vela for your reply! I'll try it out :)
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    Transformation function from ground state -> nth energy state, force applied, HO

    Hello, I found one way to do it which requires changing the Schrodinger representation into the Heisenberg representation and writing p_n(t) = <n|0>^(f) *<0|n>^(f) = <0| P_n(t)|0>^(f), where p_n(t) is the probability that the force changes the ground state into the n-th energy state...
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    Transformation function from ground state -> nth energy state, force applied, HO

    Hello Everyone! I have a question regarding a Quantum problem I am trying to solve in L. Brown's Quantum Field Theory book, Chapter 1, Problem 4.f. Homework Statement I have a question which asks me to compute [p][/n], i.e. the probability that the ground state (n=0) is brought to the...
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    Find recursion relation, ODE, to find relation between d_(n+1), d_(n), and trK^(n+1)

    I found a document online which explains the problem on page 8 of the 52 available pages. I am now just working out the induction part of the proof.. not entirely sure how they expand the espression for a_(n+1).. Link: http://krein.unica.it/~cornelis/private/PDF/IEOT/ieot_26_136.pdf [Broken]
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    Find recursion relation, ODE, to find relation between d_(n+1), d_(n), and trK^(n+1)

    Hi Voko! I'm looking at the text and at the end of the problem it says let K be an arbitrary kernel. At the end of the problem he starts his promised explanation on the "convergence of the power series in λ that rigorously defines the infinite determinant for an arbitrary kernel K(x,x')". I...
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    Find recursion relation, ODE, to find relation between d_(n+1), d_(n), and trK^(n+1)

    Hello Everyone! I have a problem I am solving through a self study project from Lowell Brown's book entitled: Quantum Field Theory". It is a math question (basically) on recursion relations. 1. Homework Statement The variational definition gives us the relation: det[1-λK] = exp{tr...
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    Find recursion relation, ODE, to find relation between d_(n+1), d_(n), and trK^(n+1)

    Hello Mentors: I posted a question 5 days ago and have recieved no reply to date. I checked and re-checked the posting rules and I think I have followed all the posting rules. Can you please tell if there is anything wrong so I can better ask my question next time? Thank you, imanbk
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    Find recursion relation, ODE, to find relation between d_(n+1), d_(n), and trK^(n+1)

    Is there anyone who can help me with this question? I'm willing to think with whoever can shed some light on how to solve this recursion relation. Thanks a bunch..
  24. I

    Find recursion relation, ODE, to find relation between d_(n+1), d_(n), and trK^(n+1)

    Hello Everyone! I have a problem I am solving through a self study project from Lowell Brown's book entitled: Quantum Field Theory". It is a math question (basically) on recursion relations. Homework Statement The variational definition gives us the relation: det[1-λK] = exp{tr...
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